A376948 G.f.: Sum_{k>=0} 2^k * x^(k^2) / Product_{j=1..k} (1 - x^j).

1, 2, 2, 2, 6, 6, 10, 10, 14, 22, 26, 34, 46, 54, 66, 82, 110, 126, 162, 194, 246, 286, 354, 410, 502, 606, 714, 842, 1014, 1190, 1418, 1658, 1950, 2278, 2666, 3090, 3646, 4198, 4882, 5634, 6558, 7534, 8754, 10002, 11558, 13230, 15218, 17322, 19910, 22702, 25914, 29466, 33606

Offset: 0

Author

Vaclav Kotesovec, Oct 10 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A003114, A032302, A376945, A376947.

Programs

Mathematica

nmax = 80; CoefficientList[Series[Sum[2^k*x^(k^2) / Product[1-x^j, {j, 1, k}], {k, 0, Sqrt[nmax]}], {x, 0, nmax}], x]

Formula

a(n) ~ (Pi^2/6 + log(2)^2)^(1/4) * exp(sqrt((Pi^2/3 + 2*log(2)^2)*n)) / (2^(3/4) * sqrt(3*Pi) * n^(3/4)).