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URL: https://oeis.org/A285293

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A285293
Expansion of Product_{k>=1} (1 + x^k)^k / (1 + x^(5*k))^(5*k).
4
1, 1, 2, 5, 8, 11, 23, 39, 58, 102, 160, 250, 392, 614, 929, 1426, 2155, 3221, 4816, 7124, 10516, 15389, 22448, 32549, 47027, 67586, 96779, 138052, 196078, 277606, 391570, 550516, 771442, 1077818, 1501214, 2084899, 2887759, 3988792, 5495381, 7552127, 10353345
OFFSET
0,3
COMMENTS
In general, if m > 1 and g.f. = Product_{k>=1} (1 + x^k)^k / (1 + x^(m*k))^(m*k), then a(n, m) ~ exp(2^(-4/3) * 3^(4/3) * (1-1/m)^(1/3) * Zeta(3)^(1/3) * n^(2/3)) * 2^(m/12 - 3/4) * (1-1/m)^(1/6) * Zeta(3)^(1/6) / (3^(1/3) * sqrt(Pi) * n^(2/3)).
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Vaclav Kotesovec)
FORMULA
a(n) ~ exp(2^(-2/3) * 3^(4/3) * 5^(-1/3) * Zeta(3)^(1/3) * n^(2/3)) * Zeta(3)^(1/6) / (3^(1/3) * 5^(1/6) * sqrt(Pi) * n^(2/3)).
MATHEMATICA
nmax = 50; CoefficientList[Series[Product[(1+x^k)^k/(1+x^(5*k))^(5*k), {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
Cf. A262736 (m=2), A262924 (m=3), A285292 (m=4).
Sequence in context: A018846 A261578 A264613 * A246442 A056661 A229883
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Apr 16 2017
STATUS
approved