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

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

Author

Seiichi Manyama, Apr 23 2018

Keywords

• sign

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