A285288 Expansion of Product_{k>=0} (1 + x^(4*k+1))^(4*k+1).

1, 1, 0, 0, 0, 5, 5, 0, 0, 9, 19, 10, 0, 13, 58, 55, 10, 17, 118, 191, 95, 26, 223, 512, 400, 116, 362, 1175, 1329, 564, 609, 2368, 3593, 2218, 1246, 4402, 8600, 7118, 3433, 7792, 18503, 19778, 10702, 13924, 37009, 49017, 32097, 27141, 69629, 111251, 88972

Offset: 0

Author

Seiichi Manyama, Apr 16 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Product_{k>=0} (1 + x^(m*k+1))^(m*k+1): A262736 (m=2), A262949 (m=3), this sequence (m=4).

Cf. A285070, A285287.

Programs

Mathematica

nmax = 50; CoefficientList[Series[Product[(1 + x^(4*k-3))^(4*k-3), {k,1,nmax}], {x,0,nmax}], x] (* Vaclav Kotesovec, Apr 16 2017 *)

Formula

a(n) = (-1)^n * A285070(n).

a(n) ~ exp(3^(4/3) * Zeta(3)^(1/3) * n^(2/3) / 4) * Zeta(3)^(1/6) / (2^(23/24) * 3^(1/3) * sqrt(Pi) * n^(2/3)). - Vaclav Kotesovec, Apr 16 2017