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

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

Offset: 0

Author

Alois P. Heinz, Oct 20 2018

Keywords

• nonn

Links

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

Crossrefs

Column k=10 of A292508.

Programs

Magma

m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)^10*(&*[1-x^j: j in [2..30]])))); // G. C. Greubel, Oct 27 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 *)

PARI

x='x+O('x^30); Vec(1/((1-x)^10*prod(j=2, 40, 1-x^j))) \\ G. C. Greubel, Oct 27 2018

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