A262949 Expansion of Product_{k>=1} (1 + x^(3*k-2))^(3*k-2).

1, 1, 0, 0, 4, 4, 0, 7, 13, 6, 10, 38, 32, 17, 74, 103, 59, 139, 266, 191, 247, 593, 581, 513, 1175, 1487, 1190, 2223, 3453, 2938, 4158, 7264, 7095, 8052, 14430, 16308, 16246, 27364, 35347, 34096, 50997, 72595, 72163, 94707, 142522, 151435, 178047, 270112

Offset: 0

Author

Vaclav Kotesovec, Oct 05 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A261612, A262879, A262884, A262924, A262948.

Programs

Mathematica

nmax=60; CoefficientList[Series[Product[(1 + x^(3*k-2))^(3*k-2),{k,1,nmax}],{x,0,nmax}],x]

Formula

a(n) ~ exp(3 * 2^(-4/3) * Zeta(3)^(1/3) * n^(2/3)) * Zeta(3)^(1/6) / (2^(7/12) * sqrt(3*Pi) * n^(2/3)).