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 1-3 of 3 results.

A285213 Expansion of Product_{k>=0} (1-x^(4*k+3))^(4*k+3).

Original entry on oeis.org

1, 0, 0, -3, 0, 0, 3, -7, 0, -1, 21, -11, 0, -21, 54, -15, 7, -96, 122, -19, 74, -311, 217, -44, 351, -768, 367, -209, 1227, -1663, 591, -989, 3402, -3225, 1156, -3609, 8289, -5815, 3053, -11096, 18015, -10176, 9466, -29593, 36249, -18454, 28960, -71093, 68438
Offset: 0

Views

Author

Seiichi Manyama, Apr 15 2017

Keywords

Links

Crossrefs

Product_{k>=0} (1-x^(m*k+m-1))^(m*k+m-1): A285069 (m=2), A285212 (m=3), this sequence (m=4), A285214 (m=5).
Cf. A285131.

Programs

  • Mathematica
    nmax = 50; CoefficientList[Series[Product[(1-x^(4*k-1))^(4*k-1), {k,1,nmax}], {x,0,nmax}], x] (* Vaclav Kotesovec, Apr 15 2017 *)
  • PARI
    x='x+O('x^100); Vec(prod(k=0, 100, (1 - x^(4*k + 3))^(4*k + 3))) \\ Indranil Ghosh, Apr 15 2017

Formula

a(n) ~ (-1)^n * exp(3^(4/3) * Zeta(3)^(1/3) * n^(2/3) / 4) * Zeta(3)^(1/6) / (2^(23/24) * 3^(1/3) * sqrt(Pi) * n^(2/3)). - Vaclav Kotesovec, Apr 17 2017

A285214 Expansion of Product_{k>=0} (1-x^(5*k+4))^(5*k+4).

Original entry on oeis.org

1, 0, 0, 0, -4, 0, 0, 0, 6, -9, 0, 0, -4, 36, -14, 0, 1, -54, 92, -19, 0, 36, -228, 202, -24, -9, 272, -702, 358, -29, -158, 1168, -1696, 598, 2, -1027, 3810, -3605, 904, 423, -4600, 10196, -6898, 1240, 2990, -15805, 24104, -12242, 822, 14005, -46090, 51376
Offset: 0

Views

Author

Seiichi Manyama, Apr 15 2017

Keywords

Links

Crossrefs

Product_{k>=0} (1-x^(m*k+m-1))^(m*k+m-1): A285069 (m=2), A285212 (m=3), A285213 (m=4), this sequence (m=5).
Cf. A285132.

Programs

  • Mathematica
    nmax = 100; CoefficientList[Series[Product[(1-x^(5*k+4))^(5*k+4), {k,0,nmax}], {x,0,nmax}], x] (* Vaclav Kotesovec, Apr 15 2017 *)
  • PARI
    x='x+O('x^100); Vec(prod(k=0, 100, (1 - x^(5*k + 4))^(5*k + 4))) \\ Indranil Ghosh, Apr 15 2017

A285247 Expansion of Product_{k>=1} (1-x^(3*k-1))^(3*k-1) * (1-x^(3*k-2))^(3*k-2).

Original entry on oeis.org

1, -1, -2, 2, -3, -2, 13, -5, -9, 35, -25, -34, 91, -78, -102, 240, -192, -233, 665, -441, -553, 1636, -1063, -1327, 3869, -2565, -3229, 8738, -6032, -7446, 19568, -13469, -16499, 43083, -29101, -35282, 93458, -61544, -74539, 198072, -128917, -155580, 412116, -267021
Offset: 0

Views

Author

Seiichi Manyama, Apr 15 2017

Keywords

Links

Crossrefs

Cf. A262923, A285050, A285212.

Programs

  • PARI
    x='x+O('x^100); Vec(prod(k=1, 100, (1 - x^(3*k - 1))^(3*k - 1)*(1 - x^(3*k - 2))^(3*k - 2))) \\ Indranil Ghosh, Apr 15 2017

Formula

Convolution inverse of A262923.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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