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.

A303387 Expansion of Product_{k>=1} ((1 - 4*x^k)/(1 + 4*x^k))^(1/4).

Original entry on oeis.org

1, -2, 0, -10, 22, -102, 244, -1270, 3360, -16886, 46160, -230670, 656550, -3238250, 9474684, -46289530, 138590342, -671116710, 2047182480, -9837322110, 30482926482, -145474988978, 456854466860, -2166890174370, 6884188144964, -32471461699594
Offset: 0

Views

Author

Seiichi Manyama, Apr 23 2018

Keywords

Links

Crossrefs

Expansion of Product_{k>=1} ((1 - 2^b*x^k)/(1 + 2^b*x^k))^(1/(2^b)): A002448 (b=0), A303345 (b=1), this sequence (b=2), A303396 (b=3).
Cf. A303360, A303402.

Programs

  • Maple
    seq(coeff(series(mul(((1-4*x^k)/(1+4*x^k))^(1/4), k = 1..n), x, n+1), x, n), n=0..25); # Muniru A Asiru, Apr 23 2018
  • PARI
    N=66; x='x+O('x^N); Vec(prod(k=1, N, ((1-4*x^k)/(1+4*x^k))^(1/4)))

Formula

a(n) ~ c * (-4)^n / n^(3/4), where c = (QPochhammer[-1, -1/4] / QPochhammer[-1/4])^(1/4) / Gamma(1/4) = 0.29599817925108933574246285.... - Vaclav Kotesovec, Apr 25 2018

A303398 Expansion of Product_{k>=1} (1 - 3*x^k)/(1 + 3*x^k).

Original entry on oeis.org

1, -6, 12, -24, 102, -312, 840, -2544, 7788, -23406, 69816, -208968, 628536, -1886712, 5654784, -16961856, 50900934, -152709936, 458084244, -1374231912, 4122828408, -12368549040, 37105252680, -111315549552, 333947845416, -1001844169854, 3005528872008
Offset: 0

Views

Author

Seiichi Manyama, Apr 23 2018

Keywords

Links

Crossrefs

Expansion of Product_{k>=1} (1 - b*x^k)/(1 + b*x^k): A002448 (b=1), A303397 (b=2), this sequence (b=3), A303402 (b=4).
Cf. A303390.

Programs

  • Maple
    N:= 100: # for a(0)..a(N)
G:= mul((1-3*x^k)/(1+3*x^k),k=1..N):
S:= series(G,x,N+1):
seq(coeff(S,x,n),n=0..N); # Robert Israel, Jul 31 2020
  • Mathematica
    nmax = 30; CoefficientList[Series[Product[(1 - 3*x^k)/(1 + 3*x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 25 2018 *)
  • PARI
    N=66; x='x+O('x^N); Vec(prod(k=1, N, (1-3*x^k)/(1+3*x^k)))

Formula

a(n) ~ c * (-3)^n, where c = QPochhammer[-1, -1/3]/QPochhammer[-1/3] = 1.1824106844873309732830080836112464096086... - Vaclav Kotesovec, Apr 25 2018
Showing 1-2 of 2 results.

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