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A285340 Expansion of Product_{k>=0} (1 + x^(5*k+4))^(5*k+4). 3
1, 0, 0, 0, 4, 0, 0, 0, 6, 9, 0, 0, 4, 36, 14, 0, 1, 54, 92, 19, 0, 36, 228, 202, 24, 9, 272, 702, 358, 29, 158, 1168, 1696, 598, 70, 1027, 3810, 3605, 904, 501, 4600, 10196, 6898, 1408, 3078, 15805, 24104, 12242, 2838, 14103, 46090, 51376, 20566, 9443, 51682 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
In general, if m > 1 and g.f. = Product_{k>=1} (1 + x^(m*k-1))^(m*k-1), then a(n, m) ~ exp(2^(-4/3) * 3^(4/3) * m^(-1/3) * Zeta(3)^(1/3) * n^(2/3)) * Zeta(3)^(1/6) / (2^(1/6 + 1/(2*m) + m/12) * 3^(1/3) * m^(1/6) * sqrt(Pi) * n^(2/3)). - Vaclav Kotesovec, Apr 17 2017
LINKS
FORMULA
a(n) ~ exp(2^(-4/3) * 3^(4/3) * 5^(-1/3) * Zeta(3)^(1/3) * n^(2/3)) * Zeta(3)^(1/6) / (2^(41/60) * 3^(1/3) * 5^(1/6) * sqrt(Pi) * n^(2/3)). - Vaclav Kotesovec, Apr 17 2017
MATHEMATICA
nmax = 50; CoefficientList[Series[Product[(1 + x^(5*k-1))^(5*k-1), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 17 2017 *)
CROSSREFS
Product_{k>=0} (1 + x^(m*k+m-1))^(m*k+m-1): A262736 (m=2), A262948 (m=3), A285339 (m=4), this sequence (m=5).
Sequence in context: A297968 A243000 A285214 * A252798 A373736 A169766
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 17 2017
STATUS
approved

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Last modified July 24 15:34 EDT 2024. Contains 374584 sequences. (Running on oeis4.)