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A285213
Expansion of Product_{k>=0} (1-x^(4*k+3))^(4*k+3).
5
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
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
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 15 2017
STATUS
approved