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.

A375062 Expansion of 1 / Sum_{k in Z} x^k / (1 - x^(5*k+1)).

Original entry on oeis.org

1, -2, 2, -1, -2, 6, -9, 9, -4, -7, 22, -34, 33, -13, -25, 71, -103, 97, -39, -69, 196, -282, 263, -102, -182, 499, -703, 645, -248, -433, 1181, -1650, 1499, -568, -988, 2652, -3660, 3294, -1240, -2129, 5681, -7790, 6960, -2595, -4438, 11732, -15959, 14161, -5252
Offset: 0

Views

Author

Seiichi Manyama, Jul 29 2024

Keywords

Crossrefs

Convolution inverse of A340456.
Cf. A375061, A375063, A375064.

Programs

  • PARI
    my(N=50, x='x+O('x^N)); Vec(1/sum(k=-N, N, x^k/(1-x^(5*k+1))))
  • PARI
    my(N=50, x='x+O('x^N)); Vec(prod(k=1, N, ((1-x^(5*k-1))*(1-x^(5*k-4)))^3/((1-x^k)*(1-x^(5*k)))))

Formula

G.f.: Product_{k>0} ((1-x^(5*k-1)) * (1-x^(5*k-4)))^3 / ((1-x^k) * (1-x^(5*k))).

A375063 Expansion of 1 / Sum_{k in Z} x^k / (1 - x^(5*k+2)).

Original entry on oeis.org

1, -1, 0, 0, -1, 3, -3, 1, 0, -3, 9, -9, 3, 1, -9, 22, -22, 9, 2, -22, 51, -51, 22, 6, -51, 108, -108, 50, 13, -108, 221, -221, 105, 29, -220, 429, -429, 212, 57, -426, 810, -810, 407, 113, -801, 1479, -1478, 759, 208, -1457, 2640, -2637, 1371, 381, -2589, 4598, -4590, 2419, 669
Offset: 0

Views

Author

Seiichi Manyama, Jul 29 2024

Keywords

Crossrefs

Convolution inverse of A340453.
Cf. A375061, A375062, A375064.

Programs

  • PARI
    my(N=60, x='x+O('x^N)); Vec(1/sum(k=-N, N, x^k/(1-x^(5*k+2))))
  • PARI
    my(N=60, x='x+O('x^N)); Vec(prod(k=1, N, (1-x^(5*k-1))*(1-x^(5*k-4))/(1-x^(5*k))^2))

Formula

G.f.: Product_{k>0} (1-x^(5*k-1)) * (1-x^(5*k-4)) / (1-x^(5*k))^2.

A375064 Expansion of 1 / Sum_{k in Z} x^(3*k) / (1 - x^(5*k+1)).

Original entry on oeis.org

1, 0, -1, -1, 0, 3, 0, -3, -3, 1, 9, 1, -9, -9, 3, 22, 3, -22, -22, 9, 51, 8, -51, -51, 21, 108, 19, -108, -108, 48, 221, 42, -221, -221, 99, 429, 86, -429, -428, 199, 810, 170, -809, -807, 378, 1479, 321, -1476, -1470, 702, 2640, 589, -2631, -2618, 1258, 4599, 1050, -4577, -4548, 2211
Offset: 0

Views

Author

Seiichi Manyama, Jul 29 2024

Keywords

Crossrefs

Convolution inverse of A340454.
Cf. A375061, A375062, A375063.

Programs

  • PARI
    my(N=60, x='x+O('x^N)); Vec(1/sum(k=-N, N, x^(3*k)/(1-x^(5*k+1))))
  • PARI
    my(N=60, x='x+O('x^N)); Vec(prod(k=1, N, (1-x^(5*k-2))*(1-x^(5*k-3))/(1-x^(5*k))^2))

Formula

G.f.: Product_{k>0} (1-x^(5*k-2)) * (1-x^(5*k-3)) / (1-x^(5*k))^2.
Showing 1-3 of 3 results.

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

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