cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A295439 a(n) = (9*n)!*(4*n)!/((8*n)!*(3*n)!*(2*n)!).

Original entry on oeis.org

1, 18, 714, 32175, 1531530, 75167268, 3762157035, 190878381495, 9781950631050, 505159120481400, 26246321470970964, 1370400311694822954, 71844872838316074315, 3779480916094795749180, 199405648908172208299875, 10547211550872819183622800, 559103542410000371874708618
Offset: 0

Views

Author

Gheorghe Coserea, Nov 23 2017

Keywords

Crossrefs

Cf. A295431.

Programs

  • Mathematica
    f[n_] := (9 n)! (4 n)!/((8 n)!*(3 n)! (2 n)!); Array[f, 17, 0] (* or *)CoefficientList[ Series[ HypergeometricPFQ[{1/9, 2/9, 4/9, 5/9, 7/9, 8/9}, {1/8, 3/8, 1/2, 5/8, 7/8}, 14348907/262144 x], {x, 0, 16}], x] (* Robert G. Wilson v, Nov 23 2017 *)

Formula

G.f.: hypergeom([1/9, 2/9, 4/9, 5/9, 7/9, 8/9], [1/8, 3/8, 1/2, 5/8, 7/8], 14348907/262144*x).
a(n) ~ 3^(15*n + 1/2) / (2^(18*n + 3/2) * sqrt(Pi*n)). - Vaclav Kotesovec, Jul 11 2025

A295441 a(n) = (9*n)!*n!/((5*n)!*(3*n)!*(2*n)!).

Original entry on oeis.org

1, 252, 204204, 191222460, 190004674860, 195022529167752, 204320742803699340, 217111359982448115765, 233102038867603938770220, 252255185100017685406870560, 274687728872310943504451521704, 300625891932698784845526074953032, 330384570746416514397560106035996940
Offset: 0

Views

Author

Gheorghe Coserea, Nov 23 2017

Keywords

Crossrefs

Cf. A295431.

Programs

  • Mathematica
    f[n_] := (9n)! n!/((5n)! (3n)! (2n)!); Array[f, 13, 0] (* or *) CoefficientList[ Series[ HypergeometricPFQ[{1/9, 2/9, 4/9, 5/9, 7/9, 8/9}, {1/5, 2/5, 1/2, 3/5, 4/5}, 14348907/12500 x], {x, 0, 12}], x] (* Robert G. Wilson v, Nov 23 2017 *)

Formula

G.f.: hypergeom([1/9, 2/9, 4/9, 5/9, 7/9, 8/9], [1/5, 2/5, 1/2, 3/5, 4/5], 14348907/12500*x).
a(n) ~ 3^(15*n + 1/2) / (2^(2*n+1) * 5^(5*n + 1/2) * sqrt(Pi*n)). - Vaclav Kotesovec, Jul 11 2025

A295443 a(n) = (18*n)!*(4*n)!/((12*n)!*(9*n)!*n!).

Original entry on oeis.org

1, 884, 1887900, 4549731788, 11560065522460, 30261639292482384, 80752826621895569988, 218391531192704847549000, 596486567319455105649942300, 1641564850552143323096960793200, 4544894671462411776709731603900400, 12644660098250754851503216626543200748
Offset: 0

Views

Author

Gheorghe Coserea, Nov 23 2017

Keywords

Crossrefs

Cf. A295431.

Programs

  • Mathematica
    f[n_] := (18n)! (4n)!/((12n)! (9n)! n!); Array[f, 12, 0] (* or *)CoefficientList[ Series[ HypergeometricPFQ[{1/18, 5/18, 7/18, 1/2, 11/18, 13/18, 17/18}, {1/12, 1/3, 5/12, 7/12, 2/3, 11/12}, 2916 x], {x, 0, 11}], x] (* Robert G. Wilson v, Nov 23 2017 *)

Formula

G.f.: hypergeom([1/18, 5/18, 7/18, 1/2, 11/18, 13/18, 17/18], [1/12, 1/3, 5/12, 7/12, 2/3, 11/12], 2916*x).
a(n) ~ 2^(2*n) * 3^(6*n - 1/2) / sqrt(Pi*n). - Vaclav Kotesovec, Jul 11 2025

A295444 a(n) = (12*n)!*(2*n)!/((9*n)!*(4*n)!*n!).

Original entry on oeis.org

1, 110, 28842, 8558480, 2679559018, 864609808860, 284430822189360, 94838361498813504, 31937586416482122090, 10837486229625098253938, 3699768692414430886979092, 1269247320827841357100956000, 437197260018920565848972207920, 151108564566619626342188272922000, 52379783376231201890753924949502656, 18202391389394546898846524075693898480
Offset: 0

Views

Author

Gheorghe Coserea, Nov 23 2017

Keywords

Crossrefs

Cf. A295431.

Programs

  • Mathematica
    f[n_] := (12n)! (2n)!/((9n)! (4n)! n!); Array[f, 14, 0] (* or *)CoefficientList[ Series[ HypergeometricPFQ[{1/12, 1/6, 5/12, 1/2, 7/12, 5/6, 11/12}, {1/9, 2/9, 4/9, 5/9, 7/9, 8/9}, 262144/729 x], {x, 0, 13}], x] (* Robert G. Wilson v, Nov 23 2017 *)

Formula

G.f.: hypergeom([1/12, 1/6, 5/12, 1/2, 7/12, 5/6, 11/12], [1/9, 2/9, 4/9, 5/9, 7/9, 8/9], 262144/729*x).
a(n) ~ 2^(18*n) / (3^(6*n + 1/2) * sqrt(Pi*n)). - Vaclav Kotesovec, Jul 11 2025

A295446 a(n) = (10*n)!*(6*n)!/((9*n)!*(5*n)!*(2*n)!).

Original entry on oeis.org

1, 30, 2090, 165648, 13873002, 1198158780, 105534616880, 9423350114880, 849915927124330, 77248168052615490, 7063878565972568340, 649143744147709730400, 59897782807583055382320, 5545885349166413944400400, 514993443497655350848314048, 47943397954241622806694753648
Offset: 0

Views

Author

Gheorghe Coserea, Nov 27 2017

Keywords

Crossrefs

Cf. A295431.

Formula

G.f.: hypergeom([1/10, 1/6, 3/10, 1/2, 7/10, 5/6, 9/10], [1/9, 2/9, 4/9, 5/9, 7/9, 8/9], 51200000/531441*x).

A295447 a(n) = (14*n)!*(3*n)!/((9*n)!*(7*n)!*n!).

Original entry on oeis.org

1, 286, 196650, 152743696, 125117624170, 105603640815036, 90864922211333424, 79239192984544856640, 69787746378451035806058, 61932198387397883017437250, 55292497255461005096459802900, 49606246898694412506503464226400, 44685036796879893398022369751697200
Offset: 0

Views

Author

Gheorghe Coserea, Nov 27 2017

Keywords

Crossrefs

Cf. A295431.

Formula

G.f.: hypergeom([1/14, 3/14, 5/14, 1/2, 9/14, 11/14, 13/14], [1/9, 2/9, 4/9, 5/9, 7/9, 8/9], 13492928512/14348907*x).

A295448 a(n) = (18*n)!*(3*n)!*(2*n)!/((9*n)!*(7*n)!*(6*n)!*n!).

Original entry on oeis.org

1, 58344, 12021607800, 2822244125414280, 700261879438261335160, 179189518952510712859732344, 46764098183514722386761235104408, 12372233944479031609487359517835891000, 3306338458421450496220314582388757069245560, 890410398621683112497449813467376431287399918400
Offset: 0

Views

Author

Gheorghe Coserea, Nov 27 2017

Keywords

Crossrefs

Cf. A295431.

Formula

G.f.: hypergeom([1/18, 5/18, 7/18, 1/2, 11/18, 13/18, 17/18], [1/7, 2/7, 3/7, 4/7, 5/7, 6/7], 235092492288/823543*x).

A295449 a(n) = (12*n)!*(2*n)!/((7*n)!*(4*n)!*(3*n)!).

Original entry on oeis.org

1, 1320, 5883768, 30159472200, 163806801888376, 918503902622731320, 5255426168361638299800, 30493180338359901231171960, 178749192506567211692013235320, 1056050334837831740009828413441344, 6277811703390706059233733243310089768, 37506272066153520595120781707670683894800, 225005811874654647839031201018894323892255640
Offset: 0

Views

Author

Gheorghe Coserea, Nov 27 2017

Keywords

Crossrefs

Cf. A295431.

Formula

G.f.: hypergeom([1/12, 1/6, 5/12, 1/2, 7/12, 5/6, 11/12], [1/7, 2/7, 3/7, 4/7, 5/7, 6/7], 5159780352/823543*x).

A295450 a(n) = (14*n)!*(6*n)!*(4*n)!/((12*n)!*(7*n)!*(3*n)!*(2*n)!).

Original entry on oeis.org

1, 52, 6300, 867724, 126266140, 18946089552, 2899163518020, 449724340595400, 70465174099304220, 11126033860866694000, 1767446723088509218800, 282158365425331981232556, 45228300709147862285651140, 7274727731093117939040291440, 1173526754722358526308356738200, 189786287381449802019915589798224
Offset: 0

Views

Author

Gheorghe Coserea, Nov 27 2017

Keywords

Crossrefs

Cf. A295431.

Formula

G.f.: hypergeom([1/14, 3/14, 5/14, 1/2, 9/14, 11/14, 13/14], [1/12, 1/3, 5/12, 7/12, 2/3, 11/12], 3294172/19683*x).

A295451 a(n) = (14*n)!*n!/((7*n)!*(5*n)!*(3*n)!).

Original entry on oeis.org

1, 24024, 2677114440, 347714586888240, 48026128282174802760, 6858171535488233066949024, 1000085563511096962480102423440, 147950885386878187684691046887599320, 22118704841920591519508406949192397599560, 3333326541499644169355299034603982863427892800
Offset: 0

Views

Author

Gheorghe Coserea, Nov 27 2017

Keywords

Crossrefs

Cf. A295431.

Formula

G.f.: hypergeom([1/14, 3/14, 5/14, 1/2, 9/14, 11/14, 13/14], [1/5, 1/3, 2/5, 3/5, 2/3, 4/5], 13492928512/84375*x).
Previous Showing 31-40 of 69 results. Next

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