A294779 Expansion of Product_{k>=1} ((1 + x^(2*k-1))/(1 - x^(2*k-1)))^(k*(k-1)/2).

1, 0, 0, 2, 0, 6, 2, 12, 12, 22, 42, 42, 114, 102, 264, 280, 564, 744, 1186, 1866, 2538, 4380, 5598, 9732, 12602, 20898, 28374, 44048, 63000, 92190, 137012, 192864, 291588, 403668, 609072, 843228, 1253978, 1752150, 2555058, 3611380, 5168778, 7371324, 10400908

Offset: 0

Author

Vaclav Kotesovec, Nov 08 2017

Keywords

• nonn

Comments

Convolution of A294777 and A294778.

Crossrefs

Cf. A206622, A292037, A294755, A294777, A294778, A294780.

Programs

Mathematica

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

Formula

a(n) ~ exp(Pi * 2^(1/4) * n^(3/4)/3 - Pi*n^(1/4) / 2^(17/4) + 3*Zeta(3) / (32*Pi^2)) / (2^(37/16) * n^(5/8)).