A280422 G.f.: Product_{k>=1} (1 + x^k) / (1 - x^(k*(k+1)/2)).

1, 2, 3, 6, 9, 13, 21, 30, 41, 59, 81, 108, 147, 195, 253, 333, 431, 549, 704, 892, 1119, 1409, 1758, 2176, 2697, 3321, 4065, 4976, 6061, 7345, 8898, 10737, 12901, 15489, 18535, 22103, 26333, 31284, 37056, 43844, 51751, 60931, 71655, 84090, 98464, 115162

Offset: 0

Author

Vaclav Kotesovec, Jan 02 2017

Keywords

• nonn

Comments

Convolution of A007294 and A000009.

Links

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

Crossrefs

Cf. A007294, A000009, A280276, A280424.

Programs

Mathematica

nmax=60; CoefficientList[Series[Product[(1+x^k)/(1-x^(k*(k+1)/2)), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ exp(sqrt(n/3)*Pi + 3^(1/4) * Zeta(3/2) * n^(1/4) - 3*Zeta(3/2)^2/(8*Pi)) / (32 * 3^(3/4) * n^(5/4)).