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A023017 Number of partitions of n into parts of 19 kinds. 2
1, 19, 209, 1710, 11495, 66880, 347681, 1649637, 7252300, 29875505, 116319938, 430976031, 1527928814, 5206792965, 17119704425, 54484060983, 168297474675, 505762373795, 1481733152790, 4239676354650, 11866652524496, 32536693623850 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 23 01:27 EDT 2019. Contains 325228 sequences. (Running on oeis4.)