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A320756 Number of partitions of n with ten kinds of 1. 2

%I

%S 1,10,56,231,782,2299,6074,14751,33454,71677,146359,286762,542042,

%T 992776,1768216,3071725,5217765,8685019,14191826,22802195,36073378,

%U 56259488,86590156,131648984,197883889,294290729,433323334,632097807,913977420,1310647455,1864817969

%N Number of partitions of n with ten kinds of 1.

%H Alois P. Heinz, <a href="/A320756/b320756.txt">Table of n, a(n) for n = 0..10000</a>

%F G.f.: 1/(1-x)^10 * 1/Product_{j>1} (1-x^j).

%F Euler transform of 10,1,1,1,... .

%F a(n) ~ 2^(5/2) * 3^4 * n^(7/2) * exp(Pi*sqrt(2*n/3)) / Pi^9. - _Vaclav Kotesovec_, Oct 24 2018

%p a:= proc(n) option remember; `if`(n=0, 1, add(

%p (numtheory[sigma](j)+9)*a(n-j), j=1..n)/n)

%p end:

%p seq(a(n), n=0..40);

%t nmax = 50; CoefficientList[Series[1/((1-x)^9 * Product[1-x^k, {k, 1, nmax}]), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Oct 24 2018 *)

%o (PARI) x='x+O('x^30); Vec(1/((1-x)^10*prod(j=2, 40, 1-x^j))) \\ _G. C. Greubel_, Oct 27 2018

%o (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

%Y Column k=10 of A292508.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Oct 20 2018

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Last modified November 27 12:51 EST 2021. Contains 349394 sequences. (Running on oeis4.)