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A023876
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G.f.: Product_{k>=1} (1 - x^k)^(-k^7).
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5
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1, 1, 129, 2316, 26956, 385017, 5512443, 70223666, 866470849, 10628564312, 126832407040, 1469751196093, 16694372607012, 186350644088784, 2042610304126944, 22007441766651756, 233482509248479425, 2441727926157182541, 25187101530316996950, 256456174925807404269
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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) ~ (35*Zeta(9))^(119/2160) * exp((3/2)^(20/9) * n^(8/9) * (35*Zeta(9))^(1/9) + Zeta'(-7)) / (2^(247/2160) * 3^(961/1080) * sqrt(Pi) * n^(1199/2160)), where Zeta(9) = A013667 = 1.0020083928260822144..., Zeta'(-7) = ((gamma + log(2*Pi) - 363/140)/30 - 315*Zeta'(8)/Pi^8)/8 = -0.00072864268015924... . - Vaclav Kotesovec, Feb 27 2015
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MAPLE
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with(numtheory):
a:= proc(n) option remember; `if`(n=0, 1,
add(add(d*d^7, d=divisors(j)) *a(n-j), j=1..n)/n)
end:
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MATHEMATICA
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max = 19; Series[ Product[1/(1 - x^k)^k^7, {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=20; x='x+O('x^m); Vec(prod(k=1, m, 1/(1-x^k)^k^7)) \\ G. C. Greubel, Oct 31 2018
(Magma) m:=20; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R! ( (&*[1/(1-x^k)^k^7: k in [1..m]]) )); // G. C. Greubel, Oct 31 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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