A280366 G.f.: Product_{k>=1} (1 + x^(k*(k+1)/2)) / (1 - x^(k*(k+1)/2)).

1, 2, 2, 4, 6, 6, 10, 14, 14, 20, 28, 30, 38, 50, 54, 66, 86, 94, 110, 138, 152, 178, 218, 238, 274, 330, 362, 412, 488, 534, 602, 710, 778, 864, 1006, 1102, 1220, 1410, 1542, 1696, 1940, 2122, 2328, 2638, 2878, 3148, 3550, 3870, 4214, 4722, 5136, 5580, 6230

Offset: 0

Author

Vaclav Kotesovec, Jan 02 2017

Keywords

• nonn

Comments

Convolution of A024940 and A007294.

Links

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

Crossrefs

Cf. A024940, A007294, A103265.

Programs

Mathematica

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

Formula

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