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A023875
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Expansion of Product_{k>=1} (1 - x^k)^(-k^6).
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5
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1, 1, 65, 794, 6970, 69251, 689896, 6309849, 55654858, 483526120, 4104495070, 33968248260, 275366110929, 2192975727284, 17169583920204, 132264358228507, 1003715206329332, 7511468689508580, 55479733165442038, 404709688656248024, 2917717129031507178
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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^(27/8) * n^(7/8) / (7*15^(1/8)) - 45*Zeta(7) / (8*Pi^6)) / (2^(29/16) * 15^(1/16) * n^(9/16)), where Zeta(7) = A013665 = 1.00834927738192... . - Vaclav Kotesovec, Feb 27 2015
a(n) = (1/n)*Sum_{k=1..n} sigma_7(k)*a(n-k). - Seiichi Manyama, Mar 05 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^6, d=divisors(j)) *a(n-j), j=1..n)/n)
end:
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MATHEMATICA
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max = 20; Series[ Product[1/(1 - x^k)^k^6, {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^6)) \\ G. C. Greubel, Oct 31 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R! ( (&*[1/(1-x^k)^k^6: k in [1..m]]) )); // G. C. Greubel, Oct 3012018
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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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