A303355 Expansion of Product_{k>0} (1+k^2*x^k)^(1/k).

1, 1, 2, 5, 5, 13, 20, 32, -2, 107, 149, 129, -108, -262, 606, 4273, -1001, -1150, -8147, -25864, 1793, 131821, 236852, 170299, -1457515, -1298382, -696074, 4852276, 13381975, 9282183, -31755860, -38912939, -155537309, 238551912, 420017788, 224666693, -1955768303

Offset: 0

Author

Seiichi Manyama, Apr 22 2018

Keywords

• sign

Comments

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

Crossrefs

Cf. A294620, A303354.

Programs

Maple

seq(coeff(series(mul((1+k^2*x^k)^(1/k), k = 1..n), x, n+1), x, n), n = 0..40); # Muniru A Asiru, Apr 22 2018

PARI

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