sequence_id
stringlengths 7
7
| sequence_name
stringlengths 4
573
| sequence
listlengths 1
348
| keywords
listlengths 1
8
| score
int64 1
2.35k
| offset_a
int64 -14,827
666,262,453B
| offset_b
int64 0
635M
⌀ | cross_references
listlengths 1
128
⌀ | former_ids
listlengths 1
3
⌀ | author
stringlengths 7
231
⌀ | timestamp
timestamp[us]date 1999-12-11 03:00:00
2025-07-19 00:40:46
| filename
stringlengths 29
29
| hash
stringlengths 32
32
|
|---|---|---|---|---|---|---|---|---|---|---|---|---|
A012801
|
exp(sec(x)*arctan(x))=1+x+1/2!*x^2+2/3!*x^3+5/4!*x^4+40/5!*x^5...
|
[
"1",
"1",
"1",
"2",
"5",
"40",
"205",
"576",
"2473",
"46208",
"475385",
"1293184",
"-2814227",
"309637120",
"5900398725",
"5786437632",
"-532397600303",
"7315622592512",
"273302104270705",
"-347058934743040",
"-68724093821987755",
"483735262691819520"
] |
[
"sign"
] | 4 | 0 | 4 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:09 |
oeisdata/seq/A012/A012801.seq
|
585ce0f87bb1a4cdee84a5ed6a1a59c4
|
A012802
|
sin(sec(x)*arctan(x))=x+20/5!*x^5-784/7!*x^7+26256/9!*x^9...
|
[
"1",
"0",
"20",
"-784",
"26256",
"-4466176",
"435729216",
"-104111460608",
"23261262303488",
"-7794968497086464",
"2988775301503636480",
"-1434421552426973564928",
"811112609409475303936000",
"-540598484103424258178285568"
] |
[
"sign"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-05-24T12:11:43 |
oeisdata/seq/A012/A012802.seq
|
12a0e45f1da7b2b59b5373b524b60104
|
A012803
|
arcsin(sec(x)*arctan(x))=x+2/3!*x^3+48/5!*x^5+1080/7!*x^7+112000/9!*x^9...
|
[
"1",
"2",
"48",
"1080",
"112000",
"9941120",
"2204340864",
"473940603136",
"177280211177472",
"70742192264802304",
"40258836839175946240",
"25560794070720075464704",
"20755313571874776988942336",
"19066653840381485832858304512"
] |
[
"nonn"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-12-27T13:50:20 |
oeisdata/seq/A012/A012803.seq
|
96f182c4922abb8a5b95504bb09f825a
|
A012804
|
tan(sec(x)*arctan(x))=x+3/3!*x^3+65/5!*x^5+2051/7!*x^7+154209/9!*x^9...
|
[
"1",
"3",
"65",
"2051",
"154209",
"14263139",
"2239618017",
"411001918627",
"110281957937729",
"33549045899804227",
"13741520797366881025",
"6244634409478025568963",
"3628509505783902549611425",
"2300839492251656581442561187"
] |
[
"sign"
] | 8 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-02-07T04:15:12 |
oeisdata/seq/A012/A012804.seq
|
f88162f1c24f1e0340708890610e5ecc
|
A012805
|
arctan(sec(x)*arctan(x))=x-1/3!*x^3+33/5!*x^5-1377/7!*x^7+99649/9!*x^9...
|
[
"1",
"-1",
"33",
"-1377",
"99649",
"-11796673",
"2017677153",
"-471591223841",
"144742585812609",
"-56447611418620289",
"27268126498786597537",
"-15985843319019939868385",
"11182140682997302960743361"
] |
[
"sign"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2016-11-28T20:47:34 |
oeisdata/seq/A012/A012805.seq
|
61b63699f5254d8df95f43b805ea7005
|
A012806
|
cos(sec(x)*arctan(x))=1-1/2!*x^2-3/4!*x^4-165/6!*x^6+1337/8!*x^8...
|
[
"1",
"-1",
"-3",
"-165",
"1337",
"-356745",
"31874997",
"-5714452653",
"1296863374193",
"-357091592679441",
"131690816886952045",
"-56304582100478416309",
"29876409015019700748969",
"-18379375710670502969514905"
] |
[
"sign"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2017-07-24T19:47:22 |
oeisdata/seq/A012/A012806.seq
|
62810b2b3030ff92cbce253b67bfaca5
|
A012807
|
sinh(sec(x)*arctan(x))=x+2/3!*x^3+40/5!*x^5+576/7!*x^7+46208/9!*x^9...
|
[
"1",
"2",
"40",
"576",
"46208",
"1293184",
"309637120",
"5786437632",
"7315622592512",
"-347058934743040",
"483735262691819520",
"-91992936989187702784",
"74923051609806418739200",
"-28841683494637052911157248"
] |
[
"sign"
] | 4 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:09 |
oeisdata/seq/A012/A012807.seq
|
ad9bb3f059bbbc96ae0f9b4fcdf35ae6
|
A012808
|
arcsinh(sec(x)*arctan(x))=x+28/5!*x^5-728/7!*x^7+54416/9!*x^9...
|
[
"1",
"0",
"28",
"-728",
"54416",
"-5676352",
"900432960",
"-193766436992",
"55349093955840",
"-20153308820338688",
"9138844606925237248",
"-5050190610067417167872",
"3343568694767924711428096",
"-2613638716122945595362951168"
] |
[
"sign"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-09-21T17:11:03 |
oeisdata/seq/A012/A012808.seq
|
2f22c0b28318a84dc976303151698ace
|
A012809
|
tanh(sec(x)*arctan(x))=x-1/3!*x^3+25/5!*x^5-1209/7!*x^7+68945/9!*x^9...
|
[
"1",
"-1",
"25",
"-1209",
"68945",
"-7692881",
"1181481769",
"-242740782153",
"66317255314721",
"-22739603323053601",
"9634203397240829625",
"-4937246969845634306905",
"3007627322996781467655025",
"-2149125294837930108279760753",
"1779707247211878394671148764873"
] |
[
"sign"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-12-29T20:04:22 |
oeisdata/seq/A012/A012809.seq
|
8f28349199805716aa3a5793044fc576
|
A012810
|
arctanh(sec(x)*arctan(x))=x+3/3!*x^3+73/5!*x^5+2779/7!*x^7...
|
[
"1",
"3",
"73",
"2779",
"260177",
"32853491",
"6787498521",
"1803655970635",
"660549566885793",
"299826162055728355",
"172107541834064358121",
"118707937911469881769147",
"98574741929922225569568241"
] |
[
"nonn"
] | 9 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2016-11-28T20:49:00 |
oeisdata/seq/A012/A012810.seq
|
24e3697a316cbf53ddc10b61972df85f
|
A012811
|
cosh(sec(x)*arctan(x))=1+1/2!*x^2+5/4!*x^4+205/6!*x^6+2473/8!*x^8...
|
[
"1",
"1",
"5",
"205",
"2473",
"475385",
"-2814227",
"5900398725",
"-532397600303",
"273302104270705",
"-68724093821987755",
"35776180280496600509",
"-16339748046588020242311",
"10552119508350355540652905"
] |
[
"sign"
] | 4 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:09 |
oeisdata/seq/A012/A012811.seq
|
09c339471ef20c3cdfc357117c538f80
|
A012812
|
sec(sec(x)*arctan(x))=1+1/2!*x^2+9/4!*x^4+345/6!*x^6+14833/8!*x^8...
|
[
"1",
"1",
"9",
"345",
"14833",
"1493265",
"158895033",
"30935964969",
"6150088646497",
"1967749424641953",
"629235472952720105",
"300014790466799113849",
"140704010339485622390865",
"93651237671421167849769905"
] |
[
"nonn"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2022-01-06T19:49:05 |
oeisdata/seq/A012/A012812.seq
|
d4546b501949a6de759ead7df61a7021
|
A012813
|
sech(sec(x)*arctan(x))=1-1/2!*x^2+1/4!*x^4-145/6!*x^6+6977/8!*x^8...
|
[
"1",
"-1",
"1",
"-145",
"6977",
"-568865",
"80708417",
"-14347965489",
"3496685652353",
"-1086579978065473",
"419435785375158145",
"-197705949756543164369",
"111488102700546889037505",
"-74151248251988209281143905"
] |
[
"sign"
] | 6 | 0 | 4 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-01-22T18:09:19 |
oeisdata/seq/A012/A012813.seq
|
a267ecaad23e7fe0a35910ece8814821
|
A012814
|
Take every 5th term of Padovan sequence A000931, beginning with the third term.
|
[
"0",
"1",
"5",
"21",
"86",
"351",
"1432",
"5842",
"23833",
"97229",
"396655",
"1618192",
"6601569",
"26931732",
"109870576",
"448227521",
"1828587033",
"7459895657",
"30433357674",
"124155792775",
"506505428836",
"2066337330754",
"8429820731201"
] |
[
"nonn",
"easy"
] | 45 | 0 | 3 |
[
"A000931",
"A012814",
"A012855"
] | null |
N. J. A. Sloane
| 2025-05-29T16:45:30 |
oeisdata/seq/A012/A012814.seq
|
34f17bf062215d1227f45249b5248f00
|
A012815
|
arcsin(sec(x)*sinh(x))=x+5/3!*x^3+85/5!*x^5+3985/7!*x^7+379625/9!*x^9...
|
[
"1",
"5",
"85",
"3985",
"379625",
"60812765",
"14677835965",
"4970543866345",
"2246783432849105",
"1306543181979948725",
"950061718955626219045",
"844558265482290124163905",
"901064938302237380563065785"
] |
[
"nonn"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2024-09-01T17:43:41 |
oeisdata/seq/A012/A012815.seq
|
455d1e6583891a240970aa20e18c6e41
|
A012816
|
E.g.f. arctan(sec(x)*sinh(x)) (odd powers only).
|
[
"1",
"2",
"-20",
"-488",
"22160",
"1616672",
"-172976960",
"-25518205568",
"4964227109120",
"1231298393825792",
"-379260096755225600",
"-142026494757146421248",
"63547531933929827962880",
"33481297996129270926221312",
"-20517021964757071715832381440",
"-14468510293983989090015078678528"
] |
[
"sign"
] | 38 | 0 | 2 |
[
"A009342",
"A012816"
] | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2024-07-25T18:02:27 |
oeisdata/seq/A012/A012816.seq
|
2494471b91bc341ed3fbc7a5501762ad
|
A012817
|
arcsinh(sec(x)*sinh(x))=x+3/3!*x^3+5/5!*x^5-217/7!*x^7+2505/9!*x^9...
|
[
"1",
"3",
"5",
"-217",
"2505",
"765963",
"-6838195",
"-9335128657",
"286658869905",
"407628336475923",
"-19130907180121195",
"-42164783730598660297",
"3124552441785986300505",
"9154657902519091515622683"
] |
[
"sign"
] | 4 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:09 |
oeisdata/seq/A012/A012817.seq
|
5f0143fc98d64503ca4ead71ff3e90cb
|
A012818
|
arctanh(sec(x)*sinh(x))=x+6/3!*x^3+140/5!*x^5+8456/7!*x^7...
|
[
"1",
"6",
"140",
"8456",
"957840",
"174293856",
"46514037440",
"17115342333056",
"8304761365213440",
"5137820023434733056",
"3947233200665413667840",
"3686931444647916864505856",
"4114664615209642258282352640"
] |
[
"nonn"
] | 7 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-02-05T15:34:18 |
oeisdata/seq/A012/A012818.seq
|
3e1fc842356c3707375db2be53f64f73
|
A012819
|
E.g.f.: sec(sec(x)*sinh(x))=1+1/2!*x^2+21/4!*x^4+837/6!*x^6+60585/8!*x^8...
|
[
"1",
"1",
"21",
"837",
"60585",
"7048489",
"1201350909",
"282008557677",
"87244033155153",
"34402407033544657",
"16843665951415524837",
"10025536600336492439061",
"7129473645057562412172537",
"5969969671887834658217008633"
] |
[
"nonn"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-08-19T17:01:18 |
oeisdata/seq/A012/A012819.seq
|
33db1845f614e63b559f4a04fc904561
|
A012820
|
sech(sec(x)*sinh(x))=1-1/2!*x^2-11/4!*x^4-37/6!*x^6+7145/8!*x^8...
|
[
"1",
"-1",
"-11",
"-37",
"7145",
"450711",
"-3070179",
"-4923539597",
"-586954253103",
"57287087552943",
"41119408518068293",
"5965331366096594059",
"-2749345524263504663367",
"-1905635088547220040309433"
] |
[
"sign"
] | 4 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:09 |
oeisdata/seq/A012/A012820.seq
|
2046d60b2cd4955936dee5b2cd8ec73f
|
A012821
|
Expansion of e.g.f. exp(sec(x)*arcsinh(x)).
|
[
"1",
"1",
"1",
"3",
"9",
"45",
"225",
"1071",
"6993",
"56697",
"467745",
"3279419",
"29529753",
"376156261",
"4297350785",
"35274762407",
"378759492257",
"8003761282417",
"122599030798017",
"853554115621363",
"8002975063348265",
"450081179390735645"
] |
[
"sign"
] | 11 | 0 | 4 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2018-02-25T20:36:54 |
oeisdata/seq/A012/A012821.seq
|
53ece7989b401f619fb24be4ae4db1cf
|
A012822
|
sin(sec(x)*arcsinh(x))=x+1/3!*x^3+5/5!*x^5-499/7!*x^7-12055/9!*x^9...
|
[
"1",
"1",
"5",
"-499",
"-12055",
"-2156871",
"-24423763",
"-27205910523",
"2396435716433",
"-1214149548475407",
"375616253471952085",
"-173184506373765285763",
"93896424495536603892025",
"-57465007424690895944339543"
] |
[
"sign"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2023-02-17T15:57:34 |
oeisdata/seq/A012/A012822.seq
|
72157215b4e7e48834718d214469dfc8
|
A012823
|
arcsin(sec(x)*arcsinh(x))=x+3/3!*x^3+53/5!*x^5+1855/7!*x^7...
|
[
"1",
"3",
"53",
"1855",
"156425",
"19537595",
"3987121981",
"1087120051511",
"408148372272017",
"193531749818796403",
"116081047496759766725",
"84538055378229508493871",
"74205177566923695709271961"
] |
[
"nonn"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2024-11-04T12:19:27 |
oeisdata/seq/A012/A012823.seq
|
e437a5d522b9ba6ff8f12a572b973a26
|
A012824
|
tan(sec(x)*arcsinh(x))=x+4/3!*x^3+80/5!*x^5+3176/7!*x^7+240128/9!*x^9...
|
[
"1",
"4",
"80",
"3176",
"240128",
"26523264",
"4329123968",
"926411177472",
"262606340440064",
"92031599216406528",
"40177149524079247360",
"20888461815920151461888",
"13005071730835628127846400",
"9394925108531366128729587712"
] |
[
"nonn"
] | 9 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-02-07T04:29:23 |
oeisdata/seq/A012/A012824.seq
|
66ce7ab6711b7574d270f8d3620b6b42
|
A012825
|
Expansion of e.g.f. of arctan(sec(x)*arcsinh(x)) (odd coefficients only).
|
[
"1",
"0",
"8",
"-392",
"20096",
"-1754368",
"241340032",
"-44833033216",
"10840711614464",
"-3348758074142720",
"1285112610745352192",
"-598690046386495291392",
"332953969072425739124736",
"-217949438999618554495500288"
] |
[
"sign"
] | 12 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2014-04-29T22:40:33 |
oeisdata/seq/A012/A012825.seq
|
68f6a056790fd6fdbf10534b7ef6d936
|
A012826
|
cos(sec(x)*arcsinh(x))=1-1/2!*x^2-7/4!*x^4-145/6!*x^6-2063/8!*x^8...
|
[
"1",
"-1",
"-7",
"-145",
"-2063",
"-128705",
"5154217",
"-510686033",
"254809389793",
"-27371394484993",
"18728499608356185",
"-5038330344345849489",
"3197858289863468529361",
"-1630641802209014177997505"
] |
[
"sign"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2018-08-04T14:54:00 |
oeisdata/seq/A012/A012826.seq
|
42088eed8aae10188eeda382c708d74c
|
A012827
|
sinh(sec(x)*arcsinh(x))=x+3/3!*x^3+45/5!*x^5+1071/7!*x^7+56697/9!*x^9...
|
[
"1",
"3",
"45",
"1071",
"56697",
"3279419",
"376156261",
"35274762407",
"8003761282417",
"853554115621363",
"450081179390735645",
"17369944484313961631",
"62576187908645427074025",
"-11407841475969056406389973"
] |
[
"sign"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2018-03-08T14:57:15 |
oeisdata/seq/A012/A012827.seq
|
fb5ef84f0db7da840a3a50e2a91f4c7a
|
A012828
|
arcsinh(sec(x)*arcsinh(x))=x+1/3!*x^3+13/5!*x^5-163/7!*x^7+12409/9!*x^9...
|
[
"1",
"1",
"13",
"-163",
"12409",
"-931207",
"131515525",
"-22736601067",
"5414338951025",
"-1621869733040399",
"608306871018022013",
"-276781704508170478131",
"150811097250449098751721",
"-96804685135198494755720343"
] |
[
"sign"
] | 4 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:09 |
oeisdata/seq/A012/A012828.seq
|
af444bbe5b96f95031d5dd2984bba4aa
|
A012829
|
tanh(sec(x)*arcsinh(x))=x-504/7!*x^7+11904/9!*x^9-1023616/11!*x^11...
|
[
"1",
"0",
"0",
"-504",
"11904",
"-1023616",
"190103680",
"-27296677888",
"6616599617536",
"-2038987281108992",
"733961541487493120",
"-333541890591777587200",
"180073909555827471974400",
"-114101788265471646305353728"
] |
[
"sign"
] | 4 | 0 | 4 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:09 |
oeisdata/seq/A012/A012829.seq
|
db767ad0afd63b5dc3417dd996933588
|
A012830
|
arctanh(sec(x)*arcsinh(x))=x+4/3!*x^3+88/5!*x^5+4184/7!*x^7...
|
[
"1",
"4",
"88",
"4184",
"398848",
"58835456",
"12993783424",
"3911934210560",
"1562951627091968",
"793328025614454784",
"501079933291827593216",
"384338283691725654392832",
"352458553186266111883247616"
] |
[
"nonn"
] | 7 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-02-05T15:36:30 |
oeisdata/seq/A012/A012830.seq
|
9fb25ad0d609f87e9e70fbeb6585a3fb
|
A012831
|
cosh(sec(x)*arcsinh(x))=1+1/2!*x^2+9/4!*x^4+225/6!*x^6+6993/8!*x^8...
|
[
"1",
"1",
"9",
"225",
"6993",
"467745",
"29529753",
"4297350785",
"378759492257",
"122599030798017",
"8002975063348265",
"9354851201922233249",
"-686072407102337430543",
"1787263355638656126843105"
] |
[
"sign"
] | 4 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:09 |
oeisdata/seq/A012/A012831.seq
|
787c1f2f91b351c3f3a6bd543609fde8
|
A012832
|
sec(sec(x)*arcsinh(x))=1+1/2!*x^2+13/4!*x^4+445/6!*x^6+24953/8!*x^8...
|
[
"1",
"1",
"13",
"445",
"24953",
"2394425",
"320731013",
"61303017269",
"15028480222577",
"4798610670513265",
"1869279471006738045",
"898190788867995464109",
"509366426382836133377513",
"343690844382622422166331305"
] |
[
"nonn"
] | 4 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:09 |
oeisdata/seq/A012/A012832.seq
|
c18acbc8a2974dcdb088dfa954ca8864
|
A012833
|
sech(sec(x)*arcsinh(x))=1-1/2!*x^2-3/4!*x^4-45/6!*x^6+2457/8!*x^8...
|
[
"1",
"-1",
"-3",
"-45",
"2457",
"-36825",
"12566037",
"-1732392389",
"313988548273",
"-92368244011185",
"30231378922437805",
"-12317648529216417629",
"6168347852710380187977",
"-3616136826996686827399305"
] |
[
"sign"
] | 4 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:09 |
oeisdata/seq/A012/A012833.seq
|
1c22fd96176153a8f0dd45d84d6b5299
|
A012834
|
arcsin(sec(x)*tanh(x))=x+2/3!*x^3+40/5!*x^5+1192/7!*x^7+87680/9!*x^9...
|
[
"1",
"2",
"40",
"1192",
"87680",
"9890432",
"1736725120",
"424537276672",
"139089326735360",
"58613115790118912",
"30905365440751206400",
"19924657840958605361152",
"15419390055940961625866240",
"14105236549373087746555707392"
] |
[
"nonn"
] | 7 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-11-21T12:46:01 |
oeisdata/seq/A012/A012834.seq
|
51e57c6c4177b9cb3164d5335a57a9a9
|
A012835
|
arctan(sec(x)*tanh(x))=x-1/3!*x^3+25/5!*x^5-761/7!*x^7+42065/9!*x^9...
|
[
"1",
"-1",
"25",
"-761",
"42065",
"-3898321",
"521329705",
"-96017526281",
"23356125062945",
"-7240133620964641",
"2786977252450841785",
"-1304375789021987253401",
"729394652578427432666225",
"-480281453260247282387992561"
] |
[
"sign"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2020-07-30T20:08:02 |
oeisdata/seq/A012/A012835.seq
|
1d2891975556425d69f25fb55384f459
|
A012836
|
arcsinh(sec(x)*tanh(x))=x+20/5!*x^5-280/7!*x^7+18000/9!*x^9...
|
[
"1",
"0",
"20",
"-280",
"18000",
"-1277760",
"159922880",
"-26119949440",
"5923118588160",
"-1705199348152320",
"619341836139299840",
"-274598298613483878400",
"146431095418622106193920",
"-92305017354779154307399680"
] |
[
"sign"
] | 4 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:09 |
oeisdata/seq/A012/A012836.seq
|
f51fd6e3f3056c766b14346543e1a440
|
A012837
|
arctanh(sec(x)*tanh(x))=x+3/3!*x^3+65/5!*x^5+2723/7!*x^7...
|
[
"1",
"3",
"65",
"2723",
"226785",
"29857443",
"5785047905",
"1544546456963",
"543833037679425",
"244141035610073283",
"136105726320473657345",
"92251004006663786578403",
"74707241586539626288837665"
] |
[
"nonn"
] | 7 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-02-05T15:39:08 |
oeisdata/seq/A012/A012837.seq
|
9e5641cb4f260d1bc78de6686d41adad
|
A012838
|
sec(sec(x)*tanh(x))=1+1/2!*x^2+9/4!*x^4+297/6!*x^6+14385/8!*x^8...
|
[
"1",
"1",
"9",
"297",
"14385",
"1207729",
"143876601",
"23841581337",
"5193194291937",
"1442318342390497",
"497436148816555113",
"208516037618871269001",
"104439610892072605613073",
"61591265237655555392072593"
] |
[
"nonn"
] | 4 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:10 |
oeisdata/seq/A012/A012838.seq
|
f59884bdcdb5176e1add845b62bef744
|
A012839
|
sech(sec(x)*tanh(x))=1-1/2!*x^2+1/4!*x^4-97/6!*x^6+2945/8!*x^8...
|
[
"1",
"-1",
"1",
"-97",
"2945",
"-148929",
"15801729",
"-1624918817",
"267458400513",
"-52723991194497",
"12773658359030017",
"-3865567565691658721",
"1370070916604727994497",
"-576252092267236760553793",
"281775954919455982384816769",
"-158211465667174544221762575521"
] |
[
"sign"
] | 6 | 0 | 4 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2017-06-20T20:15:58 |
oeisdata/seq/A012/A012839.seq
|
4c0406fa220bea116d6b463e8e75be24
|
A012840
|
exp(sec(x)*arctanh(x))=1+x+1/2!*x^2+6/3!*x^3+21/4!*x^4+120/5!*x^5...
|
[
"1",
"1",
"1",
"6",
"21",
"120",
"765",
"5376",
"46473",
"415104",
"4371225",
"48143744",
"594635613",
"7784817664",
"110691178325",
"1673986906112",
"27018807872657",
"462531126525952",
"8370279766396593",
"159859054841331712"
] |
[
"nonn"
] | 4 | 0 | 4 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:10 |
oeisdata/seq/A012/A012840.seq
|
2a7befaaf8c65e9a4d986f7523778cff
|
A012841
|
sin(sec(x)*arctanh(x))=x+4/3!*x^3+20/5!*x^5-1024/7!*x^7-147568/9!*x^9...
|
[
"1",
"4",
"20",
"-1024",
"-147568",
"-19148736",
"-2934842560",
"-551525234688",
"-127249126657792",
"-35789287036394496",
"-12158191126869847040",
"-4941201795126314303488",
"-2379230211581147229286400"
] |
[
"sign"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2022-02-15T13:23:08 |
oeisdata/seq/A012/A012841.seq
|
538be5acf505dd0c47fa043acd96d575
|
A012842
|
arcsin(sec(x)*arctanh(x))=x+6/3!*x^3+128/5!*x^5+7000/7!*x^7...
|
[
"1",
"6",
"128",
"7000",
"757760",
"137329280",
"37511412352",
"14396574922496",
"7385535722319872",
"4879586077682790400",
"4034467892180241121280",
"4080124101723746610511872",
"4954185596977233058289319936"
] |
[
"nonn"
] | 4 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:10 |
oeisdata/seq/A012/A012842.seq
|
9e7e7907fa385cb7c91be3fc332e23bc
|
A012843
|
tan(sec(x)*arctanh(x))=x+7/3!*x^3+185/5!*x^5+11471/7!*x^7...
|
[
"1",
"7",
"185",
"11471",
"1263185",
"215079159",
"52220520521",
"17117211436287",
"7278847910698529",
"3895256097472909671",
"2561265786122546675545",
"2029572906879775183011503",
"1907361016227301624675795825"
] |
[
"nonn"
] | 9 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-02-07T04:42:24 |
oeisdata/seq/A012/A012843.seq
|
37ec804c39c4bd00e1716d1903c8e3e3
|
A012844
|
arctan(sec(x)*arctanh(x))=x+3/3!*x^3-7/5!*x^5-917/7!*x^7-7183/9!*x^9...
|
[
"1",
"3",
"-7",
"-917",
"-7183",
"3803987",
"316369129",
"-40892465221",
"-12655402122271",
"1539257113273507",
"1652188971379360217",
"198029913991075323147",
"-231213557728594141960239",
"-76270663840340687485107213"
] |
[
"sign"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-09-18T11:19:36 |
oeisdata/seq/A012/A012844.seq
|
f413b35c3560c3dc8a634849c3115afe
|
A012845
|
cos(sec(x)*arctanh(x))=1-1/2!*x^2-19/4!*x^4-565/6!*x^6-24743/8!*x^8...
|
[
"1",
"-1",
"-19",
"-565",
"-24743",
"-1450985",
"-100090043",
"-5608180253",
"703874231473",
"601015521145391",
"309193460848468125",
"160230604230030181371",
"91310347371287711776777",
"58721857461984188996135495"
] |
[
"sign"
] | 7 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-11-21T12:46:01 |
oeisdata/seq/A012/A012845.seq
|
ff343405b92145594437cbeaca0b171d
|
A012846
|
sinh(sec(x)*arctanh(x))=x+6/3!*x^3+120/5!*x^5+5376/7!*x^7...
|
[
"1",
"6",
"120",
"5376",
"415104",
"48143744",
"7784817664",
"1673986906112",
"462531126525952",
"159859054841331712",
"67616604530628853760",
"34373912421215807799296",
"20685291456673100857344000"
] |
[
"nonn"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2014-10-22T15:38:05 |
oeisdata/seq/A012/A012846.seq
|
41ada3c04e3d214f8012002a9d688b6c
|
A012847
|
arcsinh(sec(x)*arctanh(x))=x+4/3!*x^3+28/5!*x^5+152/7!*x^7+6928/9!*x^9...
|
[
"1",
"4",
"28",
"152",
"6928",
"2225408",
"348750400",
"38567316608",
"5024551512320",
"2238520490011648",
"1265695140964379648",
"555587429710072952832",
"218348017328527789264896",
"124784882666107086189330432"
] |
[
"nonn"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2019-04-16T12:05:17 |
oeisdata/seq/A012/A012847.seq
|
f90771dd44545ac06f41b5458e3efbe1
|
A012848
|
tanh(sec(x)*arctanh(x))=x+3/3!*x^3-15/5!*x^5-1869/7!*x^7-88959/9!*x^9...
|
[
"1",
"3",
"-15",
"-1869",
"-88959",
"202499",
"974640433",
"190241481587",
"15481756625281",
"-5564353308576125",
"-3510791865515349775",
"-961065703006847944525",
"92025876595389114977025",
"299254465799630697304777347"
] |
[
"sign"
] | 4 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:10 |
oeisdata/seq/A012/A012848.seq
|
e54ee2e6daf4e830908666d6fd69b866
|
A012849
|
arctanh(sec(x)*arctanh(x))=x+7/3!*x^3+193/5!*x^5+13319/7!*x^7...
|
[
"1",
"7",
"193",
"13319",
"1721281",
"357281351",
"108706678273",
"45591739883975",
"25211971076762753",
"17775279702237604231",
"15562493015528998511681",
"16565188691481564795512967",
"21067308092979783990029042241"
] |
[
"nonn"
] | 8 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2015-02-05T15:41:12 |
oeisdata/seq/A012/A012849.seq
|
3da76bdf44a768e226840be19f74bc5d
|
A012850
|
cosh(sec(x)*arctanh(x))=1+1/2!*x^2+21/4!*x^4+765/6!*x^6+46473/8!*x^8...
|
[
"1",
"1",
"21",
"765",
"46473",
"4371225",
"594635613",
"110691178325",
"27018807872657",
"8370279766396593",
"3208469378545620005",
"1491108362472114151469",
"826269720877603294674201",
"538334287550086657620232905"
] |
[
"nonn"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2018-03-24T10:36:45 |
oeisdata/seq/A012/A012850.seq
|
e727f6e1ff11aa73b845e81142d1d832
|
A012851
|
sec(sec(x)*arctanh(x))=1+1/2!*x^2+25/4!*x^4+1225/6!*x^6+108113/8!*x^8...
|
[
"1",
"1",
"25",
"1225",
"108113",
"15283505",
"3167087273",
"904365439289",
"340377095938337",
"163284306442648801",
"97251848546749385145",
"70412470931263247515689",
"60905917762268697815507057",
"62032377805368358044198610705"
] |
[
"nonn"
] | 4 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:10 |
oeisdata/seq/A012/A012851.seq
|
2126bc663f1928c9b4bc3cf9ac0f8488
|
A012852
|
sech(sec(x)*arctanh(x))=1-1/2!*x^2-15/4!*x^4-225/6!*x^6+3297/8!*x^8...
|
[
"1",
"-1",
"-15",
"-225",
"3297",
"973695",
"99434577",
"3364479391",
"-1767300967487",
"-640573924497921",
"-102867079807004495",
"22939113754550703391",
"27513402069157221548193",
"11830594343212717024871295"
] |
[
"sign"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2022-08-07T17:22:25 |
oeisdata/seq/A012/A012852.seq
|
464927c370afe97b6750da68fdabaf85
|
A012853
|
Expansion of sec(x)^2+sech(x)^2 in powers of x^4.
|
[
"2",
"32",
"15872",
"44736512",
"419730685952",
"9902996106248192",
"493842960380415967232",
"46238368375619195682947072",
"7458815407441059142195019251712",
"1941965621570118224758799415904305152",
"775271967544166063656029248004350271291392",
"455362758259861772977200568672632329207841554432"
] |
[
"nonn",
"easy"
] | 16 | 0 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2014-04-23T02:02:50 |
oeisdata/seq/A012/A012853.seq
|
dd5342f5ee72a8877bca1282b770311a
|
A012854
|
Numerators of coefficients in Taylor series expansion of log(cosec(x)*log(x+1)).
|
[
"0",
"-1",
"3",
"-1",
"89",
"-19",
"61",
"-751",
"214157",
"-2857",
"2440391",
"-434293",
"4786462007",
"-8181904909",
"1166310802697",
"-5044289",
"1618597982932877",
"-5026792806787",
"3508902074919929",
"-69028763155644023",
"739712409650680415009",
"-1022779523247467",
"133929790442712217763",
"-750218743980105669781",
"129849827600028451700919961"
] |
[
"sign",
"frac"
] | 11 | 0 | 3 |
[
"A012854",
"A202379"
] | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-05-01T21:16:00 |
oeisdata/seq/A012/A012854.seq
|
be8e0b2e08f53404e15f2ce09d67bacd
|
A012855
|
a(0) = 0, a(1) = 1, a(2) = 1; thereafter a(n) = 5*a(n-1) - 4*a(n-2) + a(n-3).
|
[
"0",
"1",
"1",
"1",
"2",
"7",
"28",
"114",
"465",
"1897",
"7739",
"31572",
"128801",
"525456",
"2143648",
"8745217",
"35676949",
"145547525",
"593775046",
"2422362079",
"9882257736",
"40315615410",
"164471408185",
"670976837021",
"2737314167775",
"11167134898976"
] |
[
"nonn"
] | 40 | 0 | 5 |
[
"A000931",
"A012814",
"A012855",
"A012864",
"A060006",
"A176476"
] | null |
N. J. A. Sloane
| 2019-05-18T02:09:52 |
oeisdata/seq/A012/A012855.seq
|
ddce0e74c413efc23d22f5681a2480d4
|
A012856
|
Numerators of coefficients in Taylor series expansion of log(cosec(x)*arcsin(x)).
|
[
"0",
"1",
"1",
"193",
"25",
"4933",
"4401359",
"36740677",
"3071547701",
"23133946330973",
"329484655084859",
"21691682982342361",
"13881630720619393",
"69213549869735245153",
"3593575793538669123431",
"10240663960560618779544197",
"9484738025292216993019060741",
"8496155203670918507329390777",
"4389630332959873242573538670607401"
] |
[
"nonn",
"frac"
] | 9 | 0 | 4 |
[
"A012856",
"A202380"
] | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-05-01T21:16:00 |
oeisdata/seq/A012/A012856.seq
|
9d82389c1896d46843918764a2bcf838
|
A012857
|
Numerator of [x^(2n)] of the Taylor expansion log(cosec(x)*arctan(x))= -x^2/6 +3*x^4/20 -50*x^6/567 +203*x^8/3240 -7472*x^10/155925 +...
|
[
"0",
"-1",
"3",
"-50",
"203",
"-7472",
"319561",
"-4725019",
"8552625673",
"-2454640799284",
"16155306808034",
"-5947223237624953",
"147005475101499533",
"-2545370372470913809",
"7441717839455761431719"
] |
[
"sign",
"frac"
] | 10 | 0 | 3 |
[
"A012857",
"A175671"
] | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2011-12-20T14:50:03 |
oeisdata/seq/A012/A012857.seq
|
1889e9a0cd010a7660638467ad30cb73
|
A012858
|
Numerator of [x^(4n+2)] in the Taylor series log(cosec(x)*sinh(x))= x^2/3 +2*x^6/2835 +2*x^10/467775 +4*x^14/127702575 +..
|
[
"1",
"2",
"2",
"4",
"87734",
"310732",
"2631724",
"13785346041608",
"303257395102",
"616840823966644",
"6080390575672283210764",
"207461256206578143748856",
"79209152838572743713996404"
] |
[
"nonn",
"frac"
] | 10 | 0 | 2 |
[
"A012858",
"A069853",
"A202520"
] | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2011-12-20T14:52:36 |
oeisdata/seq/A012/A012858.seq
|
26fc9a6051e87b5f10213c4ab24b0077
|
A012859
|
Numerator of the coefficient of [x^(2n)] of the Taylor series log(cosec(x)*arcsinh(x))= x^4/15 -x^6/30 +25*x^8/1134 -269*x^10/17010 +4401359*x^12/364864500-...
|
[
"1",
"-1",
"25",
"-269",
"4401359",
"-5248651",
"3071547701",
"-6442201463",
"329484655084859",
"-85737877363717",
"13881630720619393",
"-5324119220723357533",
"3593575793538669123431",
"-31257038840658566465059",
"9484738025292216993019060741",
"-6497059861630698641837006393",
"4389630332959873242573538670607401"
] |
[
"sign",
"frac"
] | 6 | 2 | 3 |
[
"A012859",
"A202522"
] | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2011-12-20T14:55:22 |
oeisdata/seq/A012/A012859.seq
|
e741dbc0fa0a740b0bfa603d2da9dd8e
|
A012860
|
Numerators of coefficients in Taylor series expansion of log(cosec(x)*tanh(x)).
|
[
"0",
"-1",
"1",
"-61",
"17",
"-1021",
"691",
"-32762",
"929569",
"-1045394477",
"221930581",
"-651651769166",
"56963745931",
"-88306000053182",
"2093660879252671",
"-321780490474593819308",
"129848163681107301953",
"-2604961188011595075731",
"209390615747646519456961",
"-7707087027623315087276182",
"16103843159579478297227731"
] |
[
"sign",
"frac"
] | 10 | 0 | 4 |
[
"A012860",
"A202383"
] | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-05-01T21:16:00 |
oeisdata/seq/A012/A012860.seq
|
180fa3ddcfa7abe394b9d9fb66a5e8b3
|
A012861
|
Numerator of the coefficient of [x^(2n)] of the Taylor series log(cosec(x)*arctanh(x))= x^2/2 +3*x^4/20 +4*x^6/45 +203*x^8/3240 +2038*x^10/42525 +...
|
[
"1",
"3",
"4",
"203",
"2038",
"319561",
"61425307",
"8552625673",
"11620410478",
"16155306808034",
"1810024463827637",
"147005475101499533",
"139995370486066058107",
"7441717839455761431719",
"66171433716055691335387"
] |
[
"nonn",
"frac"
] | 8 | 1 | 2 |
[
"A012861",
"A202602"
] | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2011-12-21T14:13:50 |
oeisdata/seq/A012/A012861.seq
|
c9a0e05ede0a52ea0fdfb8cd0b667bdb
|
A012862
|
Numerators of coefficients in Taylor series expansion of arccosh(cosec(x)*arctanh(x)).
|
[
"1",
"7",
"211",
"87583",
"1551091",
"26136390307",
"26950515152273",
"1654341031718587",
"6818178632103851",
"5017431660958281659233",
"191065819328171102145251947",
"118321866231849362450533828517",
"14214423223280744764724946368993",
"9325196363494467475081247926762363"
] |
[
"nonn",
"frac"
] | 8 | 0 | 2 |
[
"A012862",
"A202384"
] | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-05-01T21:16:00 |
oeisdata/seq/A012/A012862.seq
|
ba86bac22be5fc8ed60e9757c33ccd59
|
A012863
|
Numerators of coefficients in Taylor series expansion of log(cotan(x)*log(x+1)).
|
[
"0",
"-1",
"-1",
"-1",
"3",
"-19",
"59",
"-751",
"174989",
"-2857",
"2249927",
"-434293",
"32401403009",
"-8181904909",
"1150205658377",
"-5044289",
"64371087485333",
"-5026792806787",
"3500507461200889",
"-69028763155644023",
"67179942704167004419",
"-1022779523247467",
"348074852007121792219",
"-750218743980105669781",
"129827894444079903690116761"
] |
[
"sign",
"frac"
] | 9 | 0 | 5 |
[
"A012863",
"A202619"
] | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-05-01T21:16:00 |
oeisdata/seq/A012/A012863.seq
|
360e5072de5198c4234e16aa4114aab9
|
A012864
|
Take every 5th term of Padovan sequence A000931, beginning with the first term.
|
[
"1",
"1",
"3",
"12",
"49",
"200",
"816",
"3329",
"13581",
"55405",
"226030",
"922111",
"3761840",
"15346786",
"62608681",
"255418101",
"1042002567",
"4250949112",
"17342153393",
"70748973084",
"288627200960",
"1177482265857",
"4803651498529",
"19596955630177"
] |
[
"nonn",
"easy",
"changed"
] | 21 | 0 | 3 |
[
"A012855",
"A012864"
] | null |
N. J. A. Sloane
| 2025-07-08T02:47:10 |
oeisdata/seq/A012/A012864.seq
|
21ed68464cb0a07e348928ec3043ee85
|
A012865
|
Numerators of coefficients in Taylor series expansion of log(cotan(x)*arcsin(x)).
|
[
"0",
"-1",
"-1",
"67",
"347",
"1417",
"590267",
"35757697",
"1103996977",
"23018952061163",
"328785573754709",
"162948371578537",
"3427455470023873621",
"69202423313396946997",
"6142449451071240707",
"174086353362000718582994221",
"37938502177281712935274975819",
"110449470605872394476263205171",
"4389621268440117526955711378765711"
] |
[
"sign",
"frac"
] | 7 | 0 | 4 |
[
"A012865",
"A202620"
] | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-05-01T21:16:00 |
oeisdata/seq/A012/A012865.seq
|
ccccf31fb0cfa245bd4a1ad3241b2e86
|
A012866
|
a(n+3) = 5*a(n+2)-4*a(n+1)+a(n).
|
[
"0",
"1",
"2",
"6",
"23",
"93",
"379",
"1546",
"6307",
"25730",
"104968",
"428227",
"1746993",
"7127025",
"29075380",
"118615793",
"483904470",
"1974134558",
"8053670703",
"32855719753",
"134038050511",
"546821044246",
"2230808738939",
"9100797568222"
] |
[
"nonn",
"easy",
"changed"
] | 15 | 0 | 3 |
[
"A012855",
"A012866"
] | null |
N. J. A. Sloane
| 2025-07-08T02:47:16 |
oeisdata/seq/A012/A012866.seq
|
637a18ec567b56ef4cc368d0824c74c9
|
A012867
|
Numerators of coefficients in Taylor series expansion of log(cotan(x)*arctan(x)).
|
[
"0",
"-2",
"1",
"-313",
"317",
"-7813",
"6895597",
"-61916737",
"10655226077",
"-41786390722733",
"613552118040217",
"-41640337444573141",
"6761598195684420293",
"-140000933764069408573",
"81775784693678733811",
"-368555295637618487393608489",
"41000094641259185671029500461",
"-243445658683280857337557514581"
] |
[
"sign",
"frac"
] | 15 | 0 | 2 |
[
"A012867",
"A202621"
] | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2018-08-31T03:36:26 |
oeisdata/seq/A012/A012867.seq
|
b365b7c7fc4fc6278aad61bd765a41f5
|
A012868
|
Numerators of coefficients in Taylor series expansion of log(cotan(x)*arcsinh(x)).
|
[
"0",
"-1",
"-1",
"-1",
"347",
"-1531",
"590267",
"-37723537",
"1103996977",
"-2158074791",
"328785573754709",
"-134852375996381",
"3427455470023873621",
"-13844935285148389217",
"6142449451071240707",
"-43761094586606903148089",
"37938502177281712935274975819",
"-110450564689571423030247983611",
"4389621268440117526955711378765711"
] |
[
"sign",
"frac"
] | 7 | 0 | 5 |
[
"A012868",
"A202622"
] | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-05-01T21:16:00 |
oeisdata/seq/A012/A012868.seq
|
b6c68e9e6eff89007a440ba8d38236c6
|
A012869
|
Numerator of [x^(2n+1)] in the Taylor series arccos(cot(x)*arcsinh(x))= x-x^3/15 +4*x^5/75 -2098*x^7/70875 +2969*x^9/141750 -35380322*x^11/2280403125 +...
|
[
"1",
"-1",
"4",
"-2098",
"2969",
"-35380322",
"8716535447",
"-1798049740063",
"19914123417989",
"-181876796289510461",
"186781215146313235681",
"-24121633940851905518327",
"40268463790986459750095639",
"-4555735317599779344180767417"
] |
[
"sign",
"frac"
] | 5 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2011-12-22T15:41:16 |
oeisdata/seq/A012/A012869.seq
|
5ea1d7ff864259e6e0d385cab4005a26
|
A012870
|
Numerator of [x^(4n+2)] in the Taylor series -log(cot(x)*tanh(x))= 2*x^2/3 +124*x^6/2835 +292*x^10/66825 +65528*x^14/127702575 -...
|
[
"2",
"124",
"292",
"65528",
"22998766228",
"26598037736",
"176612002738088",
"14801902575616661729776",
"32359766312586630724",
"169555914608329772744042648",
"26741840557472966493223060731901928"
] |
[
"nonn",
"frac"
] | 5 | 0 | 1 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2011-12-22T15:32:29 |
oeisdata/seq/A012/A012870.seq
|
99b1430f46f42867046f4a7cae41532d
|
A012871
|
Numerator of [x^(2n)] in the Taylor expansion log(cot(x)*arctanh(x))= x^4/15 +x^6/15 +317*x^8/5670 +389*x^10/8505 +6895597*x^12/182432250 +...
|
[
"1",
"1",
"317",
"389",
"6895597",
"8704831",
"10655226077",
"1657771289",
"613552118040217",
"164509043030977",
"6761598195684420293",
"10768446708299762233",
"81775784693678733811",
"463196935488177564105193",
"41000094641259185671029500461"
] |
[
"nonn",
"frac"
] | 5 | 2 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2011-12-22T15:26:28 |
oeisdata/seq/A012/A012871.seq
|
a7fba80020a08be21fe6580bf8b3718a
|
A012872
|
Expansion of e.g.f.: arcsin(sech(x)*log(x+1))=x-1/2!*x^2-6/4!*x^4+43/5!*x^5-195/6!*x^6...
|
[
"0",
"1",
"-1",
"0",
"-6",
"43",
"-195",
"1568",
"-15204",
"151373",
"-1798245",
"23630992",
"-338936730",
"5409752775",
"-93357461015",
"1736114575232",
"-34849328368680",
"747209331349305",
"-17053712316379593",
"413430901134512288"
] |
[
"sign"
] | 7 | 1 | 5 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2020-07-20T19:41:35 |
oeisdata/seq/A012/A012872.seq
|
1126165fca6198d43c328715e759ca8f
|
A012873
|
Expansion of e.g.f.: arctan(sech(x)*log(x+1))=x-1/2!*x^2-3/3!*x^3+12/4!*x^4+43/5!*x^5...
|
[
"0",
"1",
"-1",
"-3",
"12",
"43",
"-555",
"-49",
"37632",
"-154867",
"-3817845",
"45540649",
"409535148",
"-12690409929",
"-14813266559",
"3983011043675",
"-28691304331680",
"-1331245986549447",
"25689766775914647",
"419731311262402229"
] |
[
"sign"
] | 7 | 1 | 4 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2021-08-14T16:28:46 |
oeisdata/seq/A012/A012873.seq
|
00b28dfdb494200b7b2a582fff3d9e9f
|
A012874
|
Expansion of e.g.f.: arcsinh(sech(x)*log(x+1))=x-1/2!*x^2-2/3!*x^3+6/4!*x^4+33/5!*x^5...
|
[
"0",
"1",
"-1",
"-2",
"6",
"33",
"-285",
"-30",
"13580",
"-35987",
"-1418445",
"14453470",
"125352282",
"-3470151531",
"-8211284081",
"1077876542834",
"-6851721057480",
"-332020513124583",
"5842787569074567",
"104612291816295422"
] |
[
"sign"
] | 7 | 1 | 4 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2019-10-22T18:44:23 |
oeisdata/seq/A012/A012874.seq
|
da0f680546645f0c4c6fb5148f112787
|
A012875
|
Expansion of e.g.f.: arctanh(sech(x)*log(x+1))=x-1/2!*x^2+1/3!*x^3-12/4!*x^4+63/5!*x^5...
|
[
"0",
"1",
"-1",
"1",
"-12",
"63",
"-375",
"3687",
"-35056",
"378613",
"-4917645",
"67955413",
"-1033969596",
"17404675923",
"-314140085987",
"6110547378491",
"-127722302945280",
"2840677016304009",
"-67146193511101593",
"1681517639666168201"
] |
[
"sign"
] | 6 | 0 | 5 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2016-02-16T17:50:41 |
oeisdata/seq/A012/A012875.seq
|
3c20fdcb92ce160452549261726561a8
|
A012876
|
sec(sech(x)*log(x+1))=1+1/2!*x^2-3/3!*x^3+4/4!*x^4-40/5!*x^5...
|
[
"1",
"0",
"1",
"-3",
"4",
"-40",
"370",
"-2100",
"19052",
"-224712",
"2295380",
"-27161420",
"388309832",
"-5572831680",
"85093639488",
"-1453531202760",
"26088826973648",
"-491011275101888",
"9922199896825168",
"-211576194636993072"
] |
[
"sign"
] | 4 | 0 | 4 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:10 |
oeisdata/seq/A012/A012876.seq
|
eb6c65b3ffb4129906760ed1f9bb9fe1
|
A012877
|
Expansion of e.g.f.: sech(sech(x)*log(x+1))=1-1/2!*x^2+3/3!*x^3+6/4!*x^4-60/5!*x^5...
|
[
"1",
"0",
"-1",
"3",
"6",
"-60",
"-120",
"3150",
"-4592",
"-195048",
"1007520",
"18349320",
"-224812632",
"-1637441520",
"47577070632",
"97108316760",
"-12176518106048",
"54434672031488",
"3267323510285952",
"-40295881951639488",
"-953528538620154880"
] |
[
"sign"
] | 6 | 0 | 4 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2021-09-23T12:36:29 |
oeisdata/seq/A012/A012877.seq
|
b04d55a2772f75f17000802d77800e37
|
A012878
|
E.g.f.: exp(sech(x)*arcsin(x))=1+x+1/2!*x^2-1/3!*x^3-7/4!*x^4+5/5!*x^5...
|
[
"1",
"1",
"1",
"-1",
"-7",
"5",
"145",
"499",
"-2063",
"-12055",
"128705",
"2156871",
"5154217",
"-24423763",
"510686033",
"27205910523",
"254809389793",
"2396435716433",
"27371394484993",
"1214149548475407",
"18728499608356185",
"375616253471952085"
] |
[
"sign"
] | 6 | 0 | 5 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-03-25T11:48:14 |
oeisdata/seq/A012/A012878.seq
|
712306b4ab7bc4fd63bc4bf531f551f6
|
A012879
|
Expansion of e.g.f.: exp(sech(x)*arctan(x))=1+x+1/2!*x^2-4/3!*x^3-19/4!*x^4+20/5!*x^5...
|
[
"1",
"1",
"1",
"-4",
"-19",
"20",
"565",
"1024",
"-24743",
"-147568",
"1450985",
"19148736",
"-100090043",
"-2934842560",
"5608180253",
"551525234688",
"703874231473",
"-127249126657792",
"-601015521145391",
"35789287036394496",
"309193460848468125"
] |
[
"sign"
] | 6 | 0 | 4 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2017-12-22T13:43:53 |
oeisdata/seq/A012/A012879.seq
|
059e8563a6f49f0f21fd928e33b80bf4
|
A012880
|
a(n+3) = 5*a(n+2)-4*a(n+1)+a(n).
|
[
"0",
"1",
"3",
"11",
"44",
"179",
"730",
"2978",
"12149",
"49563",
"202197",
"824882",
"3365185",
"13728594",
"56007112",
"228486369",
"932131991",
"3802721591",
"15513566360",
"63289077427",
"258193843286",
"1053326473082",
"4297146069693",
"17530618299423"
] |
[
"nonn",
"easy",
"changed"
] | 10 | 0 | 3 |
[
"A012855",
"A012880"
] | null |
N. J. A. Sloane
| 2025-07-08T02:47:22 |
oeisdata/seq/A012/A012880.seq
|
fb32c389a2eeb521f5d1b096de737ae0
|
A012881
|
Expansion of e.g.f.: exp(sech(x)*arcsinh(x))=1+x+1/2!*x^2-3/3!*x^3-15/4!*x^4+5/5!*x^5...
|
[
"1",
"1",
"1",
"-3",
"-15",
"5",
"345",
"889",
"-11263",
"-82167",
"455025",
"7869301",
"-16466703",
"-906141171",
"-746021367",
"128450716913",
"480286325633",
"-22562588189167",
"-150637957014303",
"4955964959446253",
"46203820378253425"
] |
[
"sign"
] | 6 | 0 | 4 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2020-07-08T12:36:46 |
oeisdata/seq/A012/A012881.seq
|
5925a17b38460563dee9a680d63773a9
|
A012882
|
Expansion of e.g.f.: exp(sech(x)*arctanh(x))=1+x+1/2!*x^2-3/4!*x^4+20/5!*x^5+165/6!*x^6...
|
[
"1",
"1",
"1",
"0",
"-3",
"20",
"165",
"784",
"1337",
"26256",
"356745",
"4466176",
"31874997",
"435729216",
"5714452653",
"104111460608",
"1296863374193",
"23261262303488",
"357091592679441",
"7794968497086464",
"131690816886952045"
] |
[
"sign"
] | 6 | 0 | 5 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2019-02-15T16:53:05 |
oeisdata/seq/A012/A012882.seq
|
b8893f1c73ebbf375b220d0ea358b622
|
A012883
|
Numbers in which every prefix (in base 10) is 1 or a prime.
|
[
"1",
"2",
"3",
"5",
"7",
"11",
"13",
"17",
"19",
"23",
"29",
"31",
"37",
"53",
"59",
"71",
"73",
"79",
"113",
"131",
"137",
"139",
"173",
"179",
"191",
"193",
"197",
"199",
"233",
"239",
"293",
"311",
"313",
"317",
"373",
"379",
"593",
"599",
"719",
"733",
"739",
"797",
"1319",
"1373",
"1399",
"1733",
"1913",
"1931",
"1933",
"1973",
"1979",
"1993",
"1997",
"1999"
] |
[
"nonn",
"fini",
"full",
"nice",
"base"
] | 28 | 1 | 2 |
[
"A012883",
"A024770"
] | null |
Larry Calmer (larry(AT)wri.com), Simon Plouffe
| 2024-07-18T04:33:45 |
oeisdata/seq/A012/A012883.seq
|
8506e5c4931e1db556835ce8f7712509
|
A012884
|
Numbers such that every prefix and suffix is 1 or a prime.
|
[
"1",
"2",
"3",
"5",
"7",
"11",
"13",
"17",
"23",
"31",
"37",
"53",
"71",
"73",
"113",
"131",
"137",
"173",
"197",
"311",
"313",
"317",
"373",
"797",
"1373",
"1997",
"3137",
"3797",
"7331",
"73331",
"739397"
] |
[
"nonn",
"fini",
"full",
"nice",
"base"
] | 17 | 1 | 2 |
[
"A012884",
"A068669"
] | null |
Larry Calmer (larry(AT)wri.com), Simon Plouffe
| 2019-11-20T07:52:08 |
oeisdata/seq/A012/A012884.seq
|
fc4a06258400df599837870b315f252b
|
A012885
|
Suffixes of 357686312646216567629137 (all primes).
|
[
"7",
"37",
"137",
"9137",
"29137",
"629137",
"7629137",
"67629137",
"567629137",
"6567629137",
"16567629137",
"216567629137",
"6216567629137",
"46216567629137",
"646216567629137",
"2646216567629137",
"12646216567629137",
"312646216567629137",
"6312646216567629137",
"86312646216567629137"
] |
[
"nonn",
"fini",
"full",
"base"
] | 67 | 1 | 1 |
[
"A012885",
"A024785"
] | null |
Larry Calmer (larry(AT)wri.com), Simon Plouffe
| 2021-04-04T17:22:31 |
oeisdata/seq/A012/A012885.seq
|
14ad87fb9b7d73457bf076fd0732c403
|
A012886
|
a(n+3) = 5*a(n+2)-4*a(n+1)+a(n).
|
[
"1",
"2",
"3",
"8",
"30",
"121",
"493",
"2011",
"8204",
"33469",
"136540",
"557028",
"2272449",
"9270673",
"37820597",
"154292742",
"629451995",
"2567909604",
"10476032782",
"42737977489",
"174353665921",
"711292452431",
"2901785575960",
"11838111735997"
] |
[
"nonn",
"easy",
"changed"
] | 12 | 0 | 2 |
[
"A012855",
"A012886"
] | null |
N. J. A. Sloane
| 2025-07-08T02:47:28 |
oeisdata/seq/A012/A012886.seq
|
b871eb6757207d5f89d354792df63e63
|
A012887
|
exp(sin(x)+log(x+1))=1+2*x+3/2!*x^2+3/3!*x^3-3/4!*x^4-23/5!*x^5...
|
[
"1",
"2",
"3",
"3",
"-3",
"-23",
"-51",
"35",
"665",
"2017",
"-2311",
"-45133",
"-146091",
"387025",
"5568437",
"15639707",
"-99321807",
"-1058587839",
"-1821476879",
"34121660131",
"274379440173",
"-74418715727",
"-14824670374547",
"-86166831190837"
] |
[
"sign"
] | 4 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:11 |
oeisdata/seq/A012/A012887.seq
|
7f7cd31fcdb33108413a1b6496ded2e0
|
A012888
|
E.g.f.: sin(sin(x)+log(x+1))=2*x-1/2!*x^2-7/3!*x^3+18/4!*x^4-13/5!*x^5...
|
[
"0",
"2",
"-1",
"-7",
"18",
"-13",
"135",
"-1614",
"10612",
"-71215",
"637515",
"-6443034",
"67830114",
"-769960735",
"9523596355",
"-126475570464",
"1788373677960",
"-26860585215767",
"427142221117623",
"-7163185240710714",
"126244734481260190"
] |
[
"sign"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2014-05-22T13:10:31 |
oeisdata/seq/A012/A012888.seq
|
14ecbd3e4b13f0b99832b2e802eb7992
|
A012889
|
Expansion of e.g.f. tan(sin(x) + log(x+1)).
|
[
"0",
"2",
"-1",
"17",
"-54",
"677",
"-4950",
"65145",
"-752024",
"11468069",
"-176381640",
"3165529275",
"-59818647768",
"1251370749059",
"-27828301203248",
"668331142030125",
"-17039769301121760",
"462939633071828473",
"-13293952511690952000"
] |
[
"sign"
] | 8 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2018-07-27T04:35:42 |
oeisdata/seq/A012/A012889.seq
|
c4dfe8d14cee75185933b57b28cc79c9
|
A012890
|
Expansion of e.g.f. arctan(sin(x) + log(x+1)).
|
[
"0",
"2",
"-1",
"-15",
"42",
"653",
"-4890",
"-65051",
"1029560",
"10876589",
"-341906400",
"-2371373301",
"162702562440",
"368100726615",
"-103982400082288",
"393050098566969",
"84905400106831200",
"-995896955006440711"
] |
[
"sign"
] | 10 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2021-11-19T17:02:14 |
oeisdata/seq/A012/A012890.seq
|
a8b1f15eb860adff5dd57d3ab4b69c78
|
A012891
|
Expansion of e.g.f.: cos(sin(x)+log(x+1))=1-4/2!*x^2+6/3!*x^3+5/4!*x^4-10/5!*x^5...
|
[
"1",
"0",
"-4",
"6",
"5",
"-10",
"-124",
"357",
"1765",
"-20052",
"192746",
"-2608045",
"36156029",
"-495945762",
"7131236628",
"-108900686685",
"1754698305289",
"-29762316131304",
"531245939638022",
"-9965541871978821",
"196101116893487289"
] |
[
"sign"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2020-04-23T13:57:25 |
oeisdata/seq/A012/A012891.seq
|
ac2edf25940f3ec17e73c3a756bb1bf4
|
A012892
|
E.g.f.: sinh(sin(x)+log(x+1)).
|
[
"0",
"2",
"-1",
"9",
"-30",
"127",
"-855",
"5852",
"-46452",
"422101",
"-4210605",
"46275042",
"-555647334",
"7222813951",
"-101114520507",
"1516765931792",
"-24268153134120",
"412557147859433",
"-7426039662804249",
"141094759708106686"
] |
[
"sign"
] | 9 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2014-04-11T17:32:10 |
oeisdata/seq/A012/A012892.seq
|
0e0455b2bdd04a123aa918eea19283d8
|
A012893
|
arcsinh(sin(x)+log(x+1)) = 2*x-1/2!*x^2-7/3!*x^3+18/4!*x^4+243/5!*x^5...
|
[
"0",
"2",
"-1",
"-7",
"18",
"243",
"-1785",
"-19086",
"308980",
"2736225",
"-90239805",
"-495769586",
"38522052690",
"39766893593",
"-22481798964989",
"111035038388104",
"16941789968380680",
"-219516343596465735",
"-15750892172912678361"
] |
[
"sign"
] | 13 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-11-03T10:48:13 |
oeisdata/seq/A012/A012893.seq
|
57b8e13fe4787c84c7da1cdbc0337b94
|
A012894
|
tanh(sin(x)+log(x+1))=2*x-1/2!*x^2-15/3!*x^3+42/4!*x^4+397/5!*x^5...
|
[
"0",
"2",
"-1",
"-15",
"42",
"397",
"-2970",
"-18907",
"329784",
"1046557",
"-52378200",
"39245283",
"11058935448",
"-66464051873",
"-2907583542864",
"39841515891953",
"884318369944800",
"-23533039989918007",
"-273588980128387776"
] |
[
"sign"
] | 12 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-11-21T12:46:01 |
oeisdata/seq/A012/A012894.seq
|
15eda685c1e9bb98fbbc5590f233a6f5
|
A012895
|
Expansion of e.g.f.: arctanh(sin(x)+log(x+1))=2*x-1/2!*x^2+17/3!*x^3-54/4!*x^4+933/5!*x^5...
|
[
"0",
"2",
"-1",
"17",
"-54",
"933",
"-6870",
"133689",
"-1657880",
"36953013",
"-655575120",
"16777241059",
"-387038985960",
"11324556702587",
"-320046618771152",
"10626198107224309",
"-353798609245392480",
"13212399090164058153"
] |
[
"sign"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2016-05-14T09:12:45 |
oeisdata/seq/A012/A012895.seq
|
23f36f1d6e7386f9523c72e28557becf
|
A012896
|
cosh(sin(x)+log(x+1))=1+4/2!*x^2-6/3!*x^3+27/4!*x^4-150/5!*x^5...
|
[
"1",
"0",
"4",
"-6",
"27",
"-150",
"804",
"-5817",
"47117",
"-420084",
"4208294",
"-46320175",
"555501243",
"-7222426926",
"101120088944",
"-1516750292085",
"24268053812313",
"-412558206447272",
"7426037841327370",
"-141094725586446555"
] |
[
"sign"
] | 4 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2012-02-24T12:51:11 |
oeisdata/seq/A012/A012896.seq
|
fbcff55f27b4dda9f465fc7b52beb9f2
|
A012897
|
sec(sin(x)+log(x+1))=1+4/2!*x^2-6/3!*x^3+91/4!*x^4-470/5!*x^5...
|
[
"1",
"0",
"4",
"-6",
"91",
"-470",
"6004",
"-57057",
"807281",
"-10925316",
"181019254",
"-3109774415",
"60388378207",
"-1243237163142",
"27924671116008",
"-666732185288925",
"17061240258678497",
"-462532118657434344",
"13300045106193385114"
] |
[
"sign"
] | 7 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-11-21T12:46:01 |
oeisdata/seq/A012/A012897.seq
|
b5c5b57908955da86ac2c736bb1735f7
|
A012898
|
Expansion of e.g.f.: sech(sin(x)+log(x+1))=1-4/2!*x^2+6/3!*x^3+69/4!*x^4-330/5!*x^5...
|
[
"1",
"0",
"-4",
"6",
"69",
"-330",
"-2604",
"29757",
"143689",
"-3993444",
"-5337254",
"737504515",
"-2332694727",
"-175190250378",
"1654468461772",
"50077708127475",
"-960691803929007",
"-15733047012443176",
"589399300515721526"
] |
[
"sign"
] | 6 | 0 | 3 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2023-10-01T13:52:11 |
oeisdata/seq/A012/A012898.seq
|
88ff7d1c429143c71ff6f28e3afac5ef
|
A012899
|
E.g.f.: exp(arcsin(x)+log(x+1)).
|
[
"1",
"2",
"3",
"5",
"13",
"45",
"205",
"1115",
"7305",
"54305",
"464425",
"4380675",
"46230925",
"528514025",
"6635260125",
"89124741875",
"1297262292625",
"20019445694625",
"331450831284625",
"5777919619047875",
"107221860383503125",
"2083573516715965625"
] |
[
"nonn"
] | 11 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2013-05-04T02:33:25 |
oeisdata/seq/A012/A012899.seq
|
4cccf604463f75ca38380cc99f65d6de
|
A012900
|
Expansion of e.g.f.: arcsin(arcsin(x)+log(x+1))=2*x-1/2!*x^2+11/3!*x^3-30/4!*x^4+471/5!*x^5...
|
[
"0",
"2",
"-1",
"11",
"-30",
"471",
"-3015",
"58032",
"-643188",
"14520933",
"-236345445",
"6153059178",
"-133142041494",
"3956037592815",
"-106753027544163",
"3588266331746712",
"-115669410756336360",
"4361169482903542617",
"-162972793825872488073"
] |
[
"sign"
] | 6 | 0 | 2 | null | null |
Patrick Demichel (patrick.demichel(AT)hp.com)
| 2014-11-21T18:58:17 |
oeisdata/seq/A012/A012900.seq
|
37401eb8460fa586a72a30e5585de48f
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.