A023020 Number of partitions of n into parts of 22 kinds.

1, 22, 275, 2530, 18975, 122430, 702328, 3661900, 17627775, 79264900, 335937954, 1351507830, 5191041625, 19125838600, 67862904725, 232671319474, 773027485065, 2494957906100, 7839428942950, 24025993453000, 71941861591215

Offset

0,2

Comments

a(n) is Euler transform of A010861. - Alois P. Heinz, Oct 17 2008

Links

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

M. V. Movshev, A formula for the partition function of the beta-gamma system on the cone pure spinors, arXiv preprint arXiv:1602.04673 [hep-th], 2016. [Gives sequence that appears to agree with this one]

N. J. A. Sloane, Transforms [Alois P. Heinz, Oct 17 2008]

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

Formula

G.f.: Product_{m>=1} 1/(1-x^m)^22.

a(0) = 1, a(n) = (22/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*22, 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]^22, {x, 0, 30}], x] (* Indranil Ghosh, Mar 27 2017 *)

Prog

(PARI) Vec(1/eta(x)^22 + O(x^30)) \\ Indranil Ghosh, Mar 27 2017

Crossrefs

Cf. 22nd column of A144064. - Alois P. Heinz, Oct 17 2008

Sequence in context: A278153 A223116 A125434 * A022650 A172226 A004316

Adjacent sequences: A023017 A023018 A023019 * A023021 A023022 A023023

Keyword

nonn

Author

David W. Wilson

Status

approved