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A285928 Expansion of (Product_{k>0} (1 - x^(5*k)) / (1 - x^k))^5 in powers of x. 6
1, 5, 20, 65, 190, 501, 1240, 2890, 6440, 13775, 28502, 57205, 111880, 213670, 399620, 733128, 1321850, 2345340, 4100700, 7072520, 12045005, 20272465, 33746060, 55595635, 90706390, 146638756, 235016940, 373580735, 589238640, 922537655, 1434232510, 2214817165 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

In general, if m > 1 and g.f. = Product_{k>=1} ((1 - x^(m*k)) / (1 - x^k))^m, then a(n, m) ~ exp(Pi*sqrt(2*(m-1)*n/3)) * (m-1)^(1/4) / (2^(5/4) * 3^(1/4) * m^(m/2) * n^(3/4)). - Vaclav Kotesovec, Apr 30 2017

LINKS

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

FORMULA

a(0) = 1, a(n) = (5/n)*Sum_{k=1..n} A116073(k)*a(n-k) for n > 0.

a(n) ~ exp(2*Pi*sqrt(2*n/3)) / (2^(3/4) * 3^(1/4) * 5^(5/2) * n^(3/4)). - Vaclav Kotesovec, Apr 30 2017

MATHEMATICA

nmax = 40; CoefficientList[Series[Product[((1 - x^(5*k)) / (1 - x^k))^5, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 30 2017 *)

CROSSREFS

(Product_{k>0} (1 - x^(m*k)) / (1 - x^k))^m: A022567 (m=2), A285927 (m=3), A093160 (m=4), this sequence (m=5).

Cf. A035959, A285932.

Sequence in context: A195861 A001939 A100534 * A160506 A277212 A160528

Adjacent sequences:  A285925 A285926 A285927 * A285929 A285930 A285931

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Apr 28 2017

STATUS

approved

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Last modified June 24 02:56 EDT 2021. Contains 345415 sequences. (Running on oeis4.)