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A285048 Expansion of Product_{k>=0} 1/(1-x^(4*k+1))^(4*k+1). 4
1, 1, 1, 1, 1, 6, 6, 6, 6, 15, 30, 30, 30, 43, 88, 123, 123, 140, 250, 385, 455, 476, 678, 1098, 1413, 1564, 1913, 2918, 4048, 4707, 5452, 7572, 10747, 13265, 15195, 19534, 27349, 35146, 41042, 50011, 67596, 88897, 106519, 126635, 164230, 216862, 266473, 314883 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..2000 from Vaclav Kotesovec)

FORMULA

a(n) ~ 4 * Pi * 2^(25/72) * Zeta(3)^(11/72) * exp(4*c + 3 * 2^(-4/3) * Zeta(3)^(1/3) * n^(2/3)) / (sqrt(3) * Gamma(1/4)^3 * n^(47/72)), where c = Integral_{x=0..inf} ((-19/(exp(x)*96) + 1/(exp(x)*(1 - exp(-4*x))^2) - 1/(16*x^2) - 3/(16*x))/x) dx = 0.09601010361866957956805888476415949391295401812706635... - Vaclav Kotesovec, Apr 16 2017

MATHEMATICA

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

CROSSREFS

Product_{k>=0} 1/(1-x^(m*k+1))^(m*k+1): A262811 (m=2), A262947 (m=3), this sequence (m=4), A285049 (m=5).

Cf. A285070, A285287.

Sequence in context: A233550 A092937 A285287 * A265830 A116571 A054641

Adjacent sequences:  A285045 A285046 A285047 * A285049 A285050 A285051

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Apr 15 2017

STATUS

approved

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Last modified June 18 07:25 EDT 2021. Contains 345098 sequences. (Running on oeis4.)