A023016 Number of partitions of n into parts of 18 kinds.

1, 18, 189, 1482, 9576, 53676, 269325, 1235286, 5256711, 20985272, 79260723, 285139764, 982349361, 3255488082, 10416507579, 32281134120, 97154549289, 284625019800, 813310723925, 2270826800172, 6204926551824, 16615751700618

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: A246059 A288836 A341393 * A073385 A036219 A022646

Adjacent sequences: A023013 A023014 A023015 * A023017 A023018 A023019

Keyword

nonn

Author

David W. Wilson

Status

approved