A153252 - OEIS

0, 1, 2, 4, 7, 12, 19, 29, 44, 65, 94, 134, 188, 261, 358, 486, 654, 872, 1155, 1519, 1984, 2576, 3325, 4270, 5456, 6939, 8786, 11077, 13912, 17406, 21700, 26961, 33388, 41221, 50739, 62278, 76232, 93067, 113336, 137684, 166873

FORMULA

G.f.: Sum_{n >= 1} q^n(1+q)(1+q^2)...(1+q^(2n-2))/((1-q)(1-q^3)...(1-q^(2n-1))).

a(n) ~ exp(Pi*sqrt(2*n/3)) / (2^(5/2)*sqrt(3*n)). - Vaclav Kotesovec, Jun 13 2019

PROG

(PARI) lista(nn) = q = qq + O(qq^nn); gf = sum(n = 1, nn, q^n * prod(k = 1, 2*n-2, 1 + q^k) / prod(k = 1, n, 1 - q^(2*k-1))); concat(0, Vec(gf)) \\Michel Marcus, Jun 18 2013