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A023018 Number of partitions of n into parts of 20 kinds. 2
1, 20, 230, 1960, 13685, 82524, 443870, 2175800, 9869990, 41907380, 168012824, 640438680, 2334121995, 8171039800, 27580783270, 90058003200, 285253928790, 878572253720, 2636748302650, 7725084195240, 22130265931900, 62079251390180 (list; graph; refs; listen; history; text; internal format)
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: A195265 A321674 A264876 * A073386 A022648 A004315

Adjacent sequences:  A023015 A023016 A023017 * A023019 A023020 A023021

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified July 20 01:16 EDT 2019. Contains 325168 sequences. (Running on oeis4.)