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A023873
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Expansion of Product_{k>=1} (1 - x^k)^(-k^4).
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6
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1, 1, 17, 98, 490, 2411, 11940, 56093, 256274, 1140980, 4977222, 21273772, 89281011, 368408970, 1496993290, 5996312751, 23700208290, 92510062036, 356887002352, 1361671469470, 5141380256124, 19221678032134, 71190778935805, 261320839754142, 951091521384860
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) ~ exp(Pi * 2^(3/2) * 3^(2/3) * n^(5/6) / (5 * 7^(1/6)) + 3*Zeta(5) / (4*Pi^4)) / (2^(3/4) * 3^(2/3) * 7^(1/12) * n^(7/12)), where Zeta(5) = A013663 = 1.036927755143369926... . - Vaclav Kotesovec, Feb 27 2015
a(n) = (1/n)*Sum_{k=1..n} sigma_5(k)*a(n-k). - Seiichi Manyama, Mar 04 2017
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MAPLE
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with(numtheory):
a:= proc(n) option remember; `if`(n=0, 1,
add(add(d*d^4, d=divisors(j)) *a(n-j), j=1..n)/n)
end:
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MATHEMATICA
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max = 27; Series[ Product[1/(1 - x^k)^k^4, {k, 1, max}], {x, 0, max}] // CoefficientList[#, x] & (* Jean-François Alcover, Mar 05 2013 *)
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PROG
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(PARI) m=30; x='x+O('x^m); Vec(prod(k=1, m, 1/(1-x^k)^k^4)) \\ G. C. Greubel, Oct 30 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R! ( (&*[1/(1-x^k)^k^4: k in [1..m]]) )); // G. C. Greubel, Oct 30 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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