A285213 Expansion of Product_{k>=0} (1-x^(4*k+3))^(4*k+3).

1, 0, 0, -3, 0, 0, 3, -7, 0, -1, 21, -11, 0, -21, 54, -15, 7, -96, 122, -19, 74, -311, 217, -44, 351, -768, 367, -209, 1227, -1663, 591, -989, 3402, -3225, 1156, -3609, 8289, -5815, 3053, -11096, 18015, -10176, 9466, -29593, 36249, -18454, 28960, -71093, 68438

Offset

0,4

Links

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

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

Mathematica

nmax = 50; CoefficientList[Series[Product[(1-x^(4*k-1))^(4*k-1), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 15 2017 *)

Prog

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

Crossrefs

Product_{k>=0} (1-x^(m*k+m-1))^(m*k+m-1): A285069 (m=2), A285212 (m=3), this sequence (m=4), A285214 (m=5).

Cf. A285131.

Sequence in context: A341761 A181787 A318925 * A285339 A344931 A005082

Adjacent sequences: A285210 A285211 A285212 * A285214 A285215 A285216

Keyword

sign

Author

Seiichi Manyama, Apr 15 2017

Status

approved