A377077 G.f.: Sum_{k>=0} x^(7*k^2) / Product_{j=1..7*k-1} (1 - x^j).

0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 14, 20, 26, 35, 44, 58, 71, 90, 110, 136, 163, 199, 235, 282, 332, 392, 456, 535, 617, 716, 822, 946, 1079, 1236, 1402, 1596, 1806, 2046, 2306, 2606, 2929, 3299, 3704, 4163, 4667, 5241, 5870, 6585, 7378, 8273, 9268, 10397

Offset: 0

Author

Vaclav Kotesovec, Oct 15 2024

Keywords

• nonn

Links

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

Crossrefs

Column 7 of A350889.

Programs

Mathematica

nmax = 100; CoefficientList[Series[Sum[x^(7*k^2)/Product[1-x^j, {j, 1, 7*k-1}], {k, 1, Sqrt[nmax/7]}], {x, 0, nmax}], x]

Formula

a(n) ~ r^2 * (7*log(r)^2 + polylog(2, r^2))^(1/4) * exp(2*sqrt((7*log(r)^2 + polylog(2, r^2))*n)) / (2*sqrt(7*Pi*(7 - 5*r^2)) * n^(3/4)), where r = 0.839833147032421662... is the positive real root of the equation r^2 = 1 - r^7.