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A023021 Number of partitions of n into parts of 23 kinds. 6
1, 23, 299, 2852, 22126, 147407, 871838, 4680845, 23177583, 107100903, 466066181, 1923780950, 7576060505, 28601630657, 103928814438, 364712523658, 1239637963457, 4091266414235, 13139808783725, 41145568478988, 125833948024603, 376417734772625, 1102878148698235 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is Euler transform of A010862. - Alois P. Heinz, Oct 17 2008

Convolved with A000041 = A006922. - Gary W. Adamson, Jun 09 2009

LINKS

Alois P. Heinz, 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

G.f.: Product_{m>=1} 1/(1-x^m)^23.

a(0) = 1, a(n) = (23/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*23, 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[1/QPochhammer[q]^23 + O[q]^30, q] (* Jean-Fran├žois Alcover, Dec 03 2015 *)

PROG

(PARI) Vec(1/eta(x)^23 + O(x^30)) \\ Indranil Ghosh, Mar 27 2017

CROSSREFS

Cf. 23rd column of A144064. - Alois P. Heinz, Oct 17 2008

Cf. A006922, A000041. - Gary W. Adamson, Jun 09 2009

Sequence in context: A125435 A086943 A131273 * A022651 A267266 A077504

Adjacent sequences:  A023018 A023019 A023020 * A023022 A023023 A023024

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified July 20 01:17 EDT 2019. Contains 325168 sequences. (Running on oeis4.)