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.

Showing 1-6 of 6 results.

A384043 a(n) = [x^n] Product_{k=1..n} (1 + k^2*x) / (1 - k^2*x).

Original entry on oeis.org

1, 2, 50, 4188, 735600, 221302710, 101667388082, 66218673102680, 58048466179356672, 65901249246347377770, 94061755750395244537250, 164863945136411230998746612, 348110204753572939058548570000, 871547135491620353615820806025918, 2552918049709989779004770502542335650
Offset: 0

Views

Author

Vaclav Kotesovec, May 18 2025

Keywords

Crossrefs

Programs

  • Mathematica
    Table[SeriesCoefficient[Product[(1+k^2*x)/(1-k^2*x), {k, 1, n}], {x, 0, n}], {n, 0, 15}]

Formula

a(n) ~ c * d^n * n!^2 / n^(3/2), where d = 16.6871576653578743696262746377576281620174969944584774545888... and c = 0.1371163625236187865398447973928851799479072107076663329994...

A384044 a(n) = [x^n] Product_{k=1..n} (1 + k^3*x) / (1 - k^3*x).

Original entry on oeis.org

1, 2, 162, 75672, 104312000, 317309605650, 1803288012589602, 17180843554017736544, 254292459616733559570432, 5525508321588276184345621650, 168733575675064578625834983478850, 6994229599670887851052241626545021912, 382562895157136117988572795915676719695680
Offset: 0

Views

Author

Vaclav Kotesovec, May 18 2025

Keywords

Crossrefs

Programs

  • Mathematica
    Table[SeriesCoefficient[Product[(1+k^3*x)/(1-k^3*x), {k, 1, n}], {x, 0, n}], {n, 0, 12}]

Formula

a(n) ~ c * d^n * n!^3 / n^2, where d = 37.604795475701444958019770120055586495991039059348094619704... and c = 0.063895861310548119570865800164582089372152350471371583403...

A384086 a(n) = [x^n] Product_{k=1..n} ((1 + k*x)/(1 - k*x))^2.

Original entry on oeis.org

1, 4, 72, 2352, 112000, 7023540, 546991704, 50923706176, 5517464159232, 682067031126660, 94744306830613000, 14610279918692775504, 2476682373835289303424, 457771369968515293229812, 91624876032673265663215800, 19743379886572250897986694400, 4556982707091255612929249419264
Offset: 0

Views

Author

Vaclav Kotesovec, May 19 2025

Keywords

Crossrefs

Programs

  • Mathematica
    Table[SeriesCoefficient[Product[(1+k*x)^2/(1-k*x)^2, {k, 1, n}], {x, 0, n}], {n, 0, 20}]

Formula

a(n) ~ c * d^n * n! / n, where d = 15.357995623209995052090556511543938190953157405669200... and c = 0.3746298100044008083790505105262276548713201624206421...

A384087 a(n) = [x^n] Product_{k=1..n} ((1 + k*x)/(1 - k*x))^3.

Original entry on oeis.org

1, 6, 162, 7848, 552000, 51035310, 5853933666, 802178739936, 127879052859648, 23252775004089990, 4750089647035004250, 1077069265550569663416, 268437124701985949614944, 72940650531961450912140558, 21461129870889481564510048050, 6797577340761206051865208521600, 2306127185536355501260494657447936
Offset: 0

Views

Author

Vaclav Kotesovec, May 19 2025

Keywords

Crossrefs

Programs

  • Mathematica
    Table[SeriesCoefficient[Product[(1+k*x)^3/(1-k*x)^3, {k, 1, n}], {x, 0, n}], {n, 0, 16}]

Formula

a(n) ~ c * d^n * n! / n, where d = 22.56625698335414867480351407039325848948214595770919713967057... and c = 0.403760467212667768540403611728406212428403946576093482938996...

A384088 a(n) = [x^n] Product_{k=1..n} ((1 + k*x)/(1 - k*x))^4.

Original entry on oeis.org

1, 8, 288, 18528, 1728000, 211687080, 32159822688, 5835397918336, 1231573968949248, 296447550279133320, 80158746419240852000, 24057027574081163030688, 7935414295799696292767232, 2853706409310576479751168168, 1111199574070700473937862463200, 465782420445680979210397280524800
Offset: 0

Views

Author

Vaclav Kotesovec, May 19 2025

Keywords

Crossrefs

Programs

  • Mathematica
    Table[SeriesCoefficient[Product[(1+k*x)^4/(1-k*x)^4, {k, 1, n}], {x, 0, n}], {n, 0, 16}]

Formula

a(n) ~ c * d^n * n! / n, where d = 29.85915450232266280267400661836716424701025678171993103713550551... and c = 0.415660498916272367812330643610916948922178337726778287649763513...

A384093 a(n) = [x^n] Product_{k=1..n} ((1 + k^2*x)/(1 - k^2*x))^n.

Original entry on oeis.org

1, 2, 200, 100372, 141369600, 429768373550, 2413602498186776, 22580623631512230760, 326908252720653523943424, 6930499895312478999698799930, 206129722171946147890239366225000, 8311703033335976017330775929889992316, 441845483828200905036741829941273994080000
Offset: 0

Views

Author

Vaclav Kotesovec, May 19 2025

Keywords

Crossrefs

Programs

  • Mathematica
    Table[SeriesCoefficient[Product[((1+k^2*x)/(1-k^2*x))^n, {k, 1, n}], {x, 0, n}], {n, 0, 15}]

Formula

a(n) ~ 2^(n - 1/2) * exp(n + 3/2) * n^(3*n - 1/2) / (sqrt(Pi) * 3^n).
Showing 1-6 of 6 results.