A340647 G.f.: Sum_{k>=0} x^(k^2) / Product_{j=1..k} (1 - x^(2*j))^2.

1, 1, 0, 2, 1, 3, 2, 4, 5, 6, 8, 8, 14, 12, 20, 18, 31, 27, 42, 40, 60, 60, 80, 86, 111, 124, 146, 174, 199, 241, 262, 328, 353, 444, 464, 590, 620, 780, 812, 1020, 1075, 1326, 1400, 1710, 1833, 2198, 2370, 2804, 3072, 3570, 3936, 4522, 5048, 5713, 6414, 7190

Offset: 0

Author

Vaclav Kotesovec, Jan 14 2021

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
• Vaclav Kotesovec, Graph - the asymptotic ratio

Crossrefs

Cf. A000700, A006950, A340623.

Programs

Mathematica

nmax = 100; CoefficientList[Series[Sum[x^(k^2)/Product[(1-x^(2*j))^2, {j, 1, k}], {k, 0, Sqrt[nmax]}], {x, 0, nmax}], x]

Formula

a(n) = A006950(n) - A340623(n).

a(n) ~ exp(Pi*sqrt(n/2)) / (4*sqrt(2)*n).