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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

Alois P. Heinz, Table of n, a(n) for n = 0..10000

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

Adjacent sequences:  A320753 A320754 A320755 * A320757 A320758 A320759

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 20 2018

STATUS

approved

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Last modified October 22 05:36 EDT 2021. Contains 348160 sequences. (Running on oeis4.)