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A023020 Number of partitions of n into parts of 22 kinds. 2
1, 22, 275, 2530, 18975, 122430, 702328, 3661900, 17627775, 79264900, 335937954, 1351507830, 5191041625, 19125838600, 67862904725, 232671319474, 773027485065, 2494957906100, 7839428942950, 24025993453000, 71941861591215 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 23 03:00 EDT 2019. Contains 325230 sequences. (Running on oeis4.)