A265758 Expansion of Product_{k>=1} ((1 + k*x^k)/(1 - k*x^k)).

1, 2, 6, 16, 38, 88, 200, 428, 902, 1874, 3780, 7504, 14732, 28368, 54052, 101960, 189750, 349996, 640218, 1159624, 2084952, 3722008, 6593560, 11606268, 20308188, 35312170, 61065636, 105060200, 179795936, 306244136, 519291476, 876554860, 1473504846

Offset: 0

Author

Vaclav Kotesovec, Dec 15 2015

Keywords

• nonn

Comments

Convolution of A022629 and A006906.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..5000

Crossrefs

Cf. A006906, A015128, A022629, A022661, A022693, A261584.

Programs

Mathematica

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

Formula

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

c = 28711548.45004804552683870974706458425598... if mod(n,3) = 0

c = 28711547.74098394497470795294574937283075... if mod(n,3) = 1

c = 28711547.58138731567204220029302329316039... if mod(n,3) = 2.