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A320756 Number of partitions of n with ten kinds of 1. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
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
MAPLE
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);
MATHEMATICA
nmax = 50; CoefficientList[Series[1/((1-x)^9 * Product[1-x^k, {k, 1, nmax}]), {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 24 2018 *)
PROG
(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
CROSSREFS
Column k=10 of A292508.
Sequence in context: A296918 A001786 A258478 * A053309 A035040 A002889
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 20 2018
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)