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A320756
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Number of partitions of n with ten kinds of 1.
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2
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1, 10, 56, 231, 782, 2299, 6074, 14751, 33454, 71677, 146359, 286762, 542042, 992776, 1768216, 3071725, 5217765, 8685019, 14191826, 22802195, 36073378, 56259488, 86590156, 131648984, 197883889, 294290729, 433323334, 632097807, 913977420, 1310647455, 1864817969
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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)^10 * 1/Product_{j>1} (1-x^j).
Euler transform of 10,1,1,1,... .
a(n) ~ 2^(5/2) * 3^4 * n^(7/2) * exp(Pi*sqrt(2*n/3)) / Pi^9. - 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)+9)*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)^9 * 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)^10*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)^10*(&*[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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