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A320755 Number of partitions of n with nine kinds of 1. 2

%I

%S 1,9,46,175,551,1517,3775,8677,18703,38223,74682,140403,255280,450734,

%T 775440,1303509,2146040,3467254,5506807,8610369,13271183,20186110,

%U 30330668,45058828,66234905,96406840,139032605,198774473,281879613,396670035,554170514,768909964

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

%H Alois P. Heinz, <a href="/A320755/b320755.txt">Table of n, a(n) for n = 0..10000</a>

%F G.f.: 1/(1-x)^9 * 1/Product_{j>1} (1-x^j).

%F Euler transform of 9,1,1,1,... .

%F a(n) ~ 4 * 3^(7/2) * n^3 * exp(Pi*sqrt(2*n/3)) / Pi^8. - _Vaclav Kotesovec_, Oct 24 2018

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

%p (numtheory[sigma](j)+8)*a(n-j), j=1..n)/n)

%p end:

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

%t nmax = 50; CoefficientList[Series[1/((1-x)^8 * 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)^9*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)^9*(&*[1-x^j: j in [2..30]])))); // _G. C. Greubel_, Oct 27 2018

%Y Column k=9 of A292508.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Oct 20 2018

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Last modified October 23 17:37 EDT 2021. Contains 348215 sequences. (Running on oeis4.)