A285131 Expansion of Product_{k>=0} 1/(1-x^(4*k+3))^(4*k+3).

1, 0, 0, 3, 0, 0, 6, 7, 0, 10, 21, 11, 15, 42, 61, 36, 70, 150, 150, 124, 278, 441, 375, 468, 909, 1131, 1018, 1581, 2602, 2810, 2947, 4819, 6768, 6980, 8509, 13389, 16788, 17609, 23722, 34720, 40337, 44863, 63128, 85430, 95887, 114037, 159882, 202699, 227087

Offset

0,4

Links

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

Formula

a(n) ~ exp(4*c + 3 * 2^(-4/3) * Zeta(3)^(1/3) * n^(2/3)) * Zeta(3)^(11/72) / (2^(47/72) * sqrt(3) * Gamma(3/4) * n^(47/72)), where c = Integral_{x=0..inf} ((5/(exp(x)*96) + 1/(exp(3*x)*(1 - exp(-4*x))^2) - 1/(16*x^2) - 1/(16*x))/x) dx = -0.158924147180165035059952001737321408554746599955833696821824808... - Vaclav Kotesovec, Apr 15 2017

Mathematica

nmax = 100; CoefficientList[Series[Product[1/(1-x^(4*k+3))^(4*k+3), {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 15 2017 *)

Prog

(PARI) x='x+O('x^100); Vec(prod(k=0, 100, 1/(1 - x^(4*k + 3))^(4*k + 3))) \\ Indranil Ghosh, Apr 15 2017

Crossrefs

Product_{k>=0} 1/(1-x^(m*k+m-1))^(m*k+m-1): A262811 (m=2), A262946 (m=3), this sequence (m=4), A285132 (m=5).

Cf. A285213.

Sequence in context: A275689 A322015 A285311 * A110620 A270392 A060284

Adjacent sequences: A285128 A285129 A285130 * A285132 A285133 A285134

Keyword

nonn

Author

Seiichi Manyama, Apr 15 2017

Status

approved