A023018 Number of partitions of n into parts of 20 kinds.

1, 20, 230, 1960, 13685, 82524, 443870, 2175800, 9869990, 41907380, 168012824, 640438680, 2334121995, 8171039800, 27580783270, 90058003200, 285253928790, 878572253720, 2636748302650, 7725084195240, 22130265931900, 62079251390180

Offset

0,2

Comments

a(n) is Euler transform of A010859. - Alois P. Heinz, Oct 17 2008

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

N. J. A. Sloane, Transforms

Index entries for expansions of Product_{k >= 1} (1-x^k)^m

Formula

G.f.: Product_{m>=1} 1/(1-x^m)^20.

a(0) = 1, a(n) = (20/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 27 2017

Maple

with(numtheory): a:= proc(n) option remember; `if`(n=0, 1, add(add(d*20, d=divisors(j)) *a(n-j), j=1..n)/n) end: seq(a(n), n=0..40); # Alois P. Heinz, Oct 17 2008

Mathematica

CoefficientList[Series[1/QPochhammer[x]^20, {x, 0, 30}], x] (* Indranil Ghosh, Mar 27 2017 *)

Prog

(PARI) Vec(1/eta(x)^20 + O(x^30)) \\ Indranil Ghosh, Mar 27 2017

Crossrefs

20th column of A144064. - Alois P. Heinz, Oct 17 2008

Sequence in context: A321674 A264876 A341394 * A073386 A022648 A004315

Adjacent sequences: A023015 A023016 A023017 * A023019 A023020 A023021

Keyword

nonn

Author

David W. Wilson

Status

approved