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A265842
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Expansion of Product_{k>=1} (1 + k^5*x^k).
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6
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1, 1, 32, 275, 1267, 11925, 51445, 406183, 1406614, 14690040, 51144366, 251885088, 1481359033, 5108404955, 42614629915, 158222158038, 588574803125, 2360755022421, 13255325882835, 39266011999104, 325719196861377, 1031732678138822, 3791401325667894
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OFFSET
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0,3
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LINKS
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Vaclav Kotesovec, Table of n, a(n) for n = 0..2000
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FORMULA
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G.f.: exp(Sum_{k>=1} Sum_{j>=1} (-1)^(k+1)*j^(5*k)*x^(j*k)/k). - Ilya Gutkovskiy, Oct 18 2018
Conjecture: log(a(n)) ~ 5*sqrt(n/2) * (log(2*n) - 2). - Vaclav Kotesovec, Dec 27 2020
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MATHEMATICA
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nmax = 40; CoefficientList[Series[Product[1 + k^5*x^k, {k, 1, nmax}], {x, 0, nmax}], x]
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CROSSREFS
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Cf. A022629, A092484, A265839, A265840, A265841.
Sequence in context: A145711 A125369 A126527 * A248884 A223904 A122103
Adjacent sequences: A265839 A265840 A265841 * A265843 A265844 A265845
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KEYWORD
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nonn
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AUTHOR
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Vaclav Kotesovec, Dec 16 2015
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STATUS
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approved
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