login
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
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
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).
Sequence in context: A195861 A001939 A100534 * A160506 A277212 A160528
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 28 2017
STATUS
approved