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 1-2 of 2 results.

A303443 Expansion of Product_{k>=1} ((1 + 8^k*x^k)/(1 - 8^k*x^k))^(1/8^k).

Original entry on oeis.org

1, 2, 4, 50, 98, 1830, 7264, 89326, 247252, 4520886, 20225372, 241414342, 786393322, 12744704970, 62688642800, 771140700226, 2635449405522, 40907909552038, 211134761381948, 2451388697035478, 9148627707018230, 143396849321918482, 743716982801639120
Offset: 0

Views

Author

Seiichi Manyama, Apr 24 2018

Keywords

Links

Crossrefs

Cf. A303381, A303438, A303442.

Programs

  • Mathematica
    nmax = 30; CoefficientList[Series[Exp[Sum[((-1)^j - 1) / (j*(1 - 1/(8^(j-1)*x^j))), {j, 1, nmax}]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 25 2018 *)
  • PARI
    N=66; x='x+O('x^N); Vec(prod(k=1, N, ((1+8^k*x^k)/(1-8^k*x^k))^(1/8^k)))

A303490 Expansion of Product_{k>=1} ((1 - 4^k*x^k)/(1 + 4^k*x^k))^(1/4^k).

Original entry on oeis.org

1, -2, 0, -10, 22, -102, 84, -950, 3360, -18006, 21968, -162126, 613830, -2772010, 3847740, -38669210, 145735622, -567469350, 901506480, -6688787966, 27166965906, -137118406226, 234942672620, -1425038557410, 6527750118052, -27227710098826
Offset: 0

Views

Author

Seiichi Manyama, Apr 24 2018

Keywords

Links

Crossrefs

Cf. A303394, A303439, A303442, A303491.

Programs

  • Mathematica
    nmax = 30; CoefficientList[Series[Exp[Sum[(1 - (-1)^j) / (j*(1 - 1/(4^(j-1)*x^j))), {j, 1, nmax}]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 25 2018 *)
  • PARI
    N=66; x='x+O('x^N); Vec(prod(k=1, N, ((1-4^k*x^k)/(1+4^k*x^k))^(1/4^k)))

Formula

G.f.: exp(Sum_{j>=1} ((1 - (-1)^j) / (j*(1 - 1/(4^(j-1)*x^j))) )). - Vaclav Kotesovec, Apr 25 2018
Showing 1-2 of 2 results.

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