A285070 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

Offset: 0

Author

Seiichi Manyama, Apr 15 2017

Keywords

• sign

Links

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

Crossrefs

Product_{k>=0} (1-x^(m*k+1))^(m*k+1): A285069 (m=2), A285050 (m=3), this sequence (m=4), A285071 (m=5).

Cf. A285048, A285288.

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 17 2017 *)

Formula

a(n) ~ (-1)^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 17 2017