A280224 G.f.: Product_{k>=1} (1 + 2*x^(k^2)) / (1-x^k).

1, 3, 4, 7, 13, 23, 33, 51, 74, 110, 158, 222, 307, 429, 587, 792, 1065, 1423, 1877, 2470, 3227, 4196, 5416, 6963, 8899, 11344, 14384, 18158, 22840, 28647, 35786, 44552, 55295, 68423, 84422, 103879, 127457, 156009, 190481, 232007, 281934, 341879, 413640

Offset: 0

Author

Vaclav Kotesovec, Dec 29 2016

Keywords

• nonn

Comments

Convolution of A279360 and A000041.

Links

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

Crossrefs

Cf. A000041, A033461, A279360, A280204, A280225.

Programs

Mathematica

nmax=50; CoefficientList[Series[Product[(1+2*x^(k^2))/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ exp(Pi*sqrt((2*n)/3) + 3^(1/4)*c*n^(1/4)/ 2^(3/4) - 3*c^2/(32*Pi)) / (12*n), where c = -PolyLog(3/2, -2).