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A023016 Number of partitions of n into parts of 18 kinds. 2
1, 18, 189, 1482, 9576, 53676, 269325, 1235286, 5256711, 20985272, 79260723, 285139764, 982349361, 3255488082, 10416507579, 32281134120, 97154549289, 284625019800, 813310723925, 2270826800172, 6204926551824, 16615751700618 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is Euler transform of A010857. - Alois P. Heinz, Oct 17 2008

LINKS

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

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

FORMULA

a(0) = 1, a(n) = (18/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*18, 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]^18, {x, 0, 30}], x] (* Indranil Ghosh, Mar 27 2017 *)

PROG

(PARI) Vec(1/eta(x)^18 + O(x^30)) \\ Indranil Ghosh, Mar 27 2017

CROSSREFS

Cf. 18th column of A144064. - Alois P. Heinz, Oct 17 2008

Sequence in context: A036394 A246059 A288836 * A073385 A036219 A022646

Adjacent sequences:  A023013 A023014 A023015 * A023017 A023018 A023019

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified July 15 16:29 EDT 2019. Contains 325049 sequences. (Running on oeis4.)