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.

A303395 Expansion of Product_{n>=1} ((1 - (8*x)^n)/(1 + (8*x)^n))^(1/8).

Original entry on oeis.org

1, -2, -14, -140, -586, -5628, -44492, -187864, -482906, -17262828, -37958116, 65242328, -2453533124, 21817485480, 113877127592, -2570293967536, 28064994368262, 169252831757492, -188223954450804, 12624245609040632, 54083158292451540, -158891267358816264
Offset: 0

Views

Author

Seiichi Manyama, Apr 23 2018

Keywords

Crossrefs

Expansion of Product_{n>=1} ((1 + (2^b*x)^n)/(1 - (2^b)*x^n))^(1/(2^b)): A002448 (b=0), A303306 (b=1), A303394 (b=2), this sequence (b=3).
Cf. A303381.

Programs

  • PARI
    N=66; x='x+O('x^N); Vec(prod(k=1, N, ((1-(8*x)^k)/(1+(8*x)^k))^(1/8)))

A303441 Expansion of Product_{k>=1} ((1 - (2^k*x)^k)/(1 + (2^k*x)^k))^(1/2^k).

Original entry on oeis.org

1, -2, -6, -116, -7914, -2080044, -2143234268, -8791784539464, -144097582730402202, -9444444682320960008908, -2475861188239098437867827380, -2596143477450571483513272599120280, -10889030549158315918778789768740624543108
Offset: 0

Views

Author

Seiichi Manyama, Apr 24 2018

Keywords

Crossrefs

Programs

  • PARI
    N=20; x='x+O('x^N); Vec(prod(k=1, N, ((1-(2^k*x)^k)/(1+(2^k*x)^k))^(1/2^k)))

Formula

a(n) ~ -2^(n^2 - n + 1). - Vaclav Kotesovec, Apr 25 2018

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

Crossrefs

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 1-3 of 3 results.