A280276 G.f.: Product_{k>=1} (1 + x^k) / (1 - x^(k^2)).

1, 2, 3, 5, 8, 12, 17, 24, 33, 46, 62, 82, 108, 141, 182, 233, 297, 375, 472, 590, 733, 907, 1117, 1369, 1671, 2034, 2465, 2978, 3586, 4304, 5152, 6149, 7319, 8689, 10293, 12162, 14340, 16871, 19806, 23207, 27139, 31678, 36909, 42932, 49851, 57794, 66897

Offset: 0

Author

Vaclav Kotesovec, Dec 30 2016

Keywords

• nonn

Comments

Convolution of A000009 and A001156.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000009, A001156, A087154, A103265, A280277, A369570, A369574.

Programs

Mathematica

nmax=80; CoefficientList[Series[Product[(1+x^k)/(1-x^(k^2)), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ exp(Pi*sqrt(n/3) + 3^(1/4) * Zeta(3/2) * n^(1/4) / sqrt(2) - 3*Zeta(3/2)^2 / (16*Pi)) / (8*sqrt(6*Pi)*n).