A265844 Expansion of Product_{k>=1} (1 + k^2*x^k)/(1 - k^2*x^k).

1, 2, 10, 36, 118, 376, 1188, 3456, 10054, 28814, 79280, 215844, 581748, 1528456, 3987384, 10295952, 26130982, 65874532, 164661622, 406787220, 998529752, 2434022304, 5879630196, 14124455856, 33734350692, 80000820426, 188787849968, 443372664504, 1035137265552

Offset: 0

Author

Vaclav Kotesovec, Dec 16 2015

Keywords

• nonn

Comments

Convolution of A092484 and A077335.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A015128, A077335, A092484, A265758.

Programs

Mathematica

nmax = 40; CoefficientList[Series[Product[(1 + k^2*x^k)/(1 - k^2*x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ c * 3^(2*n/3), where

c = 33024.782174678163138510272317... if mod(n,3) = 0

c = 33024.230416953709449028604542... if mod(n,3) = 1

c = 33024.292470246596667257649964... if mod(n,3) = 2.