A376622 G.f.: Sum_{k>=0} x^(k*(k+1)) / Product_{j=1..k} (1 - x^(2*j-1))^2.

1, 0, 1, 2, 3, 4, 6, 8, 10, 14, 18, 22, 30, 38, 46, 60, 74, 90, 114, 138, 167, 206, 248, 298, 360, 430, 511, 612, 726, 854, 1014, 1192, 1396, 1644, 1918, 2236, 2610, 3032, 3516, 4076, 4714, 5436, 6274, 7220, 8288, 9522, 10906, 12476, 14270, 16282, 18556, 21138, 24038

Offset: 0

Author

Vaclav Kotesovec, Sep 30 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A376542, A376581, A376624, A376628.

Programs

Mathematica

nmax=60; CoefficientList[Series[Sum[x^(k*(k+1))/Product[1-x^(2*j-1), {j, 1, k}]^2, {k, 0, Sqrt[nmax]}], {x, 0, nmax}], x]

Formula

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

a(n) ~ (5 - sqrt(5)) * exp(Pi*sqrt(2*n/5)) / (8*5^(3/4)*sqrt(n)).