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.

A285070 Expansion of Product_{k>=0} (1-x^(4*k+1))^(4*k+1).

Original entry on oeis.org

1, -1, 0, 0, 0, -5, 5, 0, 0, -9, 19, -10, 0, -13, 58, -55, 10, -17, 118, -191, 95, -26, 223, -512, 400, -116, 362, -1175, 1329, -564, 609, -2368, 3593, -2218, 1246, -4402, 8600, -7118, 3433, -7792, 18503, -19778, 10702, -13924, 37009, -49017, 32097, -27141
Offset: 0

Views

Author

Seiichi Manyama, Apr 15 2017

Keywords

Links

Crossrefs

Product_{k>=0} (1-x^(m*k+1))^(m*k+1): A285069 (m=2), A285050 (m=3), this sequence (m=4), A285071 (m=5).
Cf. A285048, A285288.

Programs

  • Mathematica
    nmax = 50; CoefficientList[Series[Product[(1-x^(4*k-3))^(4*k-3), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 17 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

A285071 Expansion of Product_{k>=0} (1-x^(5*k+1))^(5*k+1).

Original entry on oeis.org

1, -1, 0, 0, 0, 0, -6, 6, 0, 0, 0, -11, 26, -15, 0, 0, -16, 82, -86, 20, 0, -21, 172, -316, 180, -15, -26, 328, -872, 790, -226, -25, 538, -2043, 2681, -1310, 130, 843, -4184, 7426, -5390, 1365, 1158, -7855, 18067, -17705, 7185, 798, -13701, 39468, -50030
Offset: 0

Views

Author

Seiichi Manyama, Apr 15 2017

Keywords

Links

Crossrefs

Product_{k>=0} (1-x^(m*k+1))^(m*k+1): A285069 (m=2), A285050 (m=3), A285070 (m=4), this sequence (m=5).
Cf. A285049, A285338.

Programs

  • Mathematica
    nmax = 50; CoefficientList[Series[Product[(1-x^(5*k-4))^(5*k-4), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 17 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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