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.

A303394 Expansion of Product_{n>=1} ((1 - (4*x)^n)/(1 + (4*x)^n))^(1/4).

Original entry on oeis.org

1, -2, -6, -28, -26, -156, -476, 968, 11526, -16172, 139724, 791928, 1315548, 12772840, 31004424, -105335920, 1058225606, 2239259700, -3700870212, 29301955992, -4944685836, -526686535112, 1134044530040, 4057865621232, -13063873857124, -113573062924024
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), this sequence (b=2), A303395 (b=3).
Cf. A303361.

Programs

  • PARI
    N=66; x='x+O('x^N); Vec(prod(k=1, N, ((1-(4*x)^k)/(1+(4*x)^k))^(1/4)))

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

A303491 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, 0, -42, 86, -1638, 1428, -71286, 218592, -3941590, 5374096, -187901262, 661408902, -10769651242, 18007942140, -597519823962, 2262843922694, -34034727280806, 65527429637360, -1858398841872062, 7543997928104274, -118580678725935186
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/(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)))

Formula

G.f.: exp(Sum_{j>=1} ((1 - (-1)^j) / (j*(1 - 1/(8^(j-1)*x^j))) )). - Vaclav Kotesovec, Apr 25 2018
Showing 1-3 of 3 results.