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

1, 9, 46, 175, 551, 1517, 3775, 8677, 18703, 38223, 74682, 140403, 255280, 450734, 775440, 1303509, 2146040, 3467254, 5506807, 8610369, 13271183, 20186110, 30330668, 45058828, 66234905, 96406840, 139032605, 198774473, 281879613, 396670035, 554170514, 768909964

Offset

0,2

Links

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

Formula

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

Euler transform of 9,1,1,1,... .

a(n) ~ 4 * 3^(7/2) * n^3 * exp(Pi*sqrt(2*n/3)) / Pi^8. - Vaclav Kotesovec, Oct 24 2018

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      (numtheory[sigma](j)+8)*a(n-j), j=1..n)/n)
    end:
seq(a(n), n=0..40);

Mathematica

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

Crossrefs

Column k=9 of A292508.

Sequence in context: A260513 A001781 A258477 * A053308 A201458 A034487

Adjacent sequences: A320752 A320753 A320754 * A320756 A320757 A320758

Keyword

nonn

Author

Alois P. Heinz, Oct 20 2018

Status

approved