A307484 Expansion of Product_{k>=1} 1/(1+x^k)^((-1)^k*k^2).

1, 1, -4, 5, 3, -17, 33, -61, 67, 63, -392, 803, -1070, 898, 482, -4449, 11362, -18630, 21105, -11067, -24871, 103562, -227004, 359040, -417697, 266106, 312987, -1578543, 3635615, -6157911, 8155892, -7689028, 1502546, 14707881, -44539735, 87849728, -136927058, 171008704

Offset: 0

Author

Seiichi Manyama, Apr 10 2019

Keywords

• sign

Comments

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = (-1)^n * n^2, g(n) = -1.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Product_{k>=1} 1/(1+x^k)^((-1)^k*k^b): A029838 (b=0), A284467 (b=1), this sequence (b=2).

Cf. A177155, A307462.

Programs

Mathematica

m = 37; CoefficientList[Series[Product[1/(1+x^k)^((-1)^k*k^2), {k, 1, m}], {x, 0, m}], x] (* Amiram Eldar, May 14 2021 *)
nmax = 40; CoefficientList[Series[Product[(1 + x^(2*k - 1))^((2*k - 1)^2)/(1 + x^(2*k))^(4*k^2), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, May 14 2021 *)

PARI

N=66; x='x+O('x^N); Vec(1/prod(k=1, N, (1+x^k)^((-1)^k*k^2)))