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.

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

A303402 Expansion of Product_{k>=1} (1 - 4*x^k)/(1 + 4*x^k).

Original entry on oeis.org

1, -8, 24, -72, 344, -1416, 5400, -21576, 87000, -348296, 1390872, -5560776, 22253784, -89025672, 356055960, -1424186568, 5696931032, -22787865096, 91150729368, -364602357960, 1458412314456, -5833651510536, 23334594559128, -93338369011272, 373353522099288
Offset: 0

Views

Author

Seiichi Manyama, Apr 23 2018

Keywords

Crossrefs

Expansion of Product_{k>=1} (1 - b*x^k)/(1 + b*x^k): A002448 (b=1), A303397 (b=2), A303398 (b=3), this sequence (b=4).
Cf. A303387, A303391.

Programs

  • Mathematica
    nmax = 30; CoefficientList[Series[Product[(1 - 4*x^k)/(1 + 4*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, (1-4*x^k)/(1+4*x^k)))

Formula

a(n) ~ c * (-4)^n, where c = QPochhammer[-1, -1/4]/QPochhammer[-1/4] = 1.3264181585010678966173808329272239860188791629... - Vaclav Kotesovec, Apr 25 2018
Showing 1-2 of 2 results.

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