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.

Previous Showing 11-14 of 14 results.

A022699 Expansion of Product_{m>=1} 1/(1 + m*q^m)^7.

Original entry on oeis.org

1, -7, 14, -7, 49, -203, 217, -295, 1365, -2667, 4214, -8519, 16842, -38570, 69012, -104433, 240758, -493374, 786835, -1434601, 2842567, -5272206, 9205546, -16034312, 29916572, -55466005, 95595395, -163656780
Offset: 0

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Crossrefs

Column k=7 of A297325.

Programs

  • Mathematica
    With[{nmax = 50}, CoefficientList[Series[Product[(1 + k*q^k)^-7, {k, 1, nmax}], {q, 0, nmax}], q]] (* G. C. Greubel, Jul 19 2018 *)
  • PARI
    m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+n*q^n)^-7)) \\ G. C. Greubel, Jul 19 2018

Formula

G.f.: exp(-7*Sum_{j>=1} Sum_{k>=1} (-1)^(j+1)*k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 08 2018

A022700 Expansion of Product_{m>=1} 1/(1 + m*q^m)^8.

Original entry on oeis.org

1, -8, 20, -16, 58, -288, 424, -464, 2035, -4816, 7364, -15008, 32030, -69152, 135352, -217840, 460537, -1012000, 1704176, -3043120, 6200086, -11737792, 21029184, -37602016, 70312646, -132822480, 235883988, -412277440
Offset: 0

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Column k=8 of A297325.

Programs

  • Mathematica
    With[{nmax = 50}, CoefficientList[Series[Product[(1 + k*q^k)^-8, {k, 1, nmax}], {q, 0, nmax}], q]] (* G. C. Greubel, Jul 19 2018 *)
  • PARI
    m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+n*q^n)^-8)) \\ G. C. Greubel, Jul 19 2018

Formula

G.f.: exp(-8*Sum_{j>=1} Sum_{k>=1} (-1)^(j+1)*k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 08 2018

A022701 Expansion of Product_{m>=1} 1/(1 + m*q^m)^9.

Original entry on oeis.org

1, -9, 27, -30, 72, -387, 738, -801, 2889, -8119, 13005, -25038, 57735, -122643, 247788, -432786, 862497, -1944657, 3520721, -6191280, 12743919, -24916977, 45349101, -83116206, 156731304, -299550636, 547421607
Offset: 0

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Column k=9 of A297325.

Programs

  • Mathematica
    With[{nmax = 50}, CoefficientList[Series[Product[(1 + k*q^k)^-9, {k, 1, nmax}], {q, 0, nmax}], q]] (* G. C. Greubel, Jul 19 2018 *)
  • PARI
    m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+n*q^n)^-9)) \\ G. C. Greubel, Jul 19 2018

Formula

G.f.: exp(-9*Sum_{j>=1} Sum_{k>=1} (-1)^(j+1)*k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 08 2018

A022716 Expansion of Product_{m>=1} (1+m*q^m)^-24.

Original entry on oeis.org

1, -24, 252, -1520, 5982, -18240, 57320, -198192, 604389, -1567840, 4210116, -12229632, 32349958, -77844000, 196563240, -510760752, 1233110610, -2871650184, 6899741020, -16499031456, 37934952672, -86122235648
Offset: 0

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Comments

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 24, g(n) = -n. - Seiichi Manyama, Dec 30 2017

Crossrefs

Column k=24 of A297325.

Programs

  • Mathematica
    With[{nmax = 50}, CoefficientList[Series[Product[(1 + k*q^k)^-24, {k, 1, nmax}], {q, 0, nmax}], q]] (* G. C. Greubel, Jul 20 2018 *)
  • PARI
    m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+n*q^n)^-24)) \\ G. C. Greubel, Jul 20 2018
Previous Showing 11-14 of 14 results.