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A320755
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Number of partitions of n with nine kinds of 1.
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2
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1, 9, 46, 175, 551, 1517, 3775, 8677, 18703, 38223, 74682, 140403, 255280, 450734, 775440, 1303509, 2146040, 3467254, 5506807, 8610369, 13271183, 20186110, 30330668, 45058828, 66234905, 96406840, 139032605, 198774473, 281879613, 396670035, 554170514, 768909964
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: 1/(1-x)^9 * 1/Product_{j>1} (1-x^j).
Euler transform of 9,1,1,1,... .
a(n) ~ 4 * 3^(7/2) * n^3 * exp(Pi*sqrt(2*n/3)) / Pi^8. - Vaclav Kotesovec, Oct 24 2018
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 1, add(
(numtheory[sigma](j)+8)*a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..40);
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MATHEMATICA
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nmax = 50; CoefficientList[Series[1/((1-x)^8 * Product[1-x^k, {k, 1, nmax}]), {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 24 2018 *)
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PROG
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(PARI) x='x+O('x^30); Vec(1/((1-x)^9*prod(j=2, 40, 1-x^j))) \\ G. C. Greubel, Oct 27 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)^9*(&*[1-x^j: j in [2..30]])))); // G. C. Greubel, Oct 27 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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STATUS
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approved
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