A307460 Expansion of Product_{k>=1} (1-x^k)^((-1)^k*k^2).

1, 1, -3, 6, -4, -15, 54, -87, 63, 79, -405, 912, -1363, 1193, 510, -4900, 12512, -21582, 26512, -16540, -24585, 113682, -255045, 419931, -519210, 377176, 267957, -1703694, 4090424, -7179222, 9895981, -9897664, 3337614, 14790666, -49171217, 100903743

Offset: 0

Author

Seiichi Manyama, Apr 09 2019

Keywords

• sign

Comments

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

Links

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

Crossrefs

Product_{k>=1} (1-x^k)^((-1)^k*k^b): A010054 (b=0), A281781 (b=1), this sequence (b=2).

Cf. A266964, A283263, A307462.

Programs

Mathematica

nmax = 40; CoefficientList[Series[Product[(1 - x^k)^((-1)^k*k^2), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 09 2019 *)

PARI

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