A023017 Number of partitions of n into parts of 19 kinds.

1, 19, 209, 1710, 11495, 66880, 347681, 1649637, 7252300, 29875505, 116319938, 430976031, 1527928814, 5206792965, 17119704425, 54484060983, 168297474675, 505762373795, 1481733152790, 4239676354650, 11866652524496, 32536693623850

Offset

0,2

Comments

a(n) is Euler transform of A010858. - 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

a(0) = 1, a(n) = (19/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*19, 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]^19, {x, 0, 30}], x] (* Indranil Ghosh, Mar 27 2017 *)

Prog

(PARI) Vec(1/eta(x)^19 + O(x^30)) \\ Indranil Ghosh, Mar 27 2017

Crossrefs

19th column of A144064. - Alois P. Heinz, Oct 17 2008

Sequence in context: A125407 A289423 A278556 * A022647 A032613 A199132

Adjacent sequences: A023014 A023015 A023016 * A023018 A023019 A023020

Keyword

nonn

Author

David W. Wilson

Status

approved