A301518 a(n) = [x^n] Product_{k>=1} (1 + x^(k^2))^n.

1, 1, 1, 1, 5, 26, 91, 246, 589, 1468, 4226, 13311, 41471, 122864, 351184, 1001876, 2920957, 8698612, 26070130, 77707056, 229959130, 679050870, 2011457295, 5986185690, 17866178695, 53343031301, 159149943668, 474683353849, 1416730630936, 4233405443596

Offset: 0

Author

Vaclav Kotesovec, Mar 23 2018

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A033461, A281790, A291649, A300974.

Programs

Mathematica

Table[SeriesCoefficient[Product[(1 + x^(k^2))^n, {k, 1, n}], {x, 0, n}], {n, 0, 30}]

Formula

a(n) ~ c * d^n / sqrt(n), where d = 3.04074590736461391963643911... and c = 0.2268848664201836146769277...