A023019 Number of partitions of n into parts of 21 kinds.

1, 21, 252, 2233, 16170, 100926, 560945, 2837418, 13266099, 57994475, 239170239, 937026279, 3507380170, 12601619226, 43628951025, 146036139347, 473924014599, 1494785958435, 4591920193357, 13764656869425, 40328218603134

Offset

0,2

Comments

a(n) is the Euler transform of A010860. - 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) = (21/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*21, 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]^21, {x, 0, 30}], x] (* Indranil Ghosh, Mar 27 2017 *)

Prog

(PARI) Vec(1/eta(x)^21 + O(x^30)) \\ Indranil Ghosh, Mar 27 2017

Crossrefs

Cf. 21st column of A144064. - Alois P. Heinz, Oct 17 2008

Sequence in context: A165099 A165108 A282923 * A036220 A022649 A165094

Adjacent sequences: A023016 A023017 A023018 * A023020 A023021 A023022

Keyword

nonn

Author

David W. Wilson, Jun 14 1998

Status

approved