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A023021 Number of partitions of n into parts of 23 kinds. 6

%I

%S 1,23,299,2852,22126,147407,871838,4680845,23177583,107100903,

%T 466066181,1923780950,7576060505,28601630657,103928814438,

%U 364712523658,1239637963457,4091266414235,13139808783725,41145568478988,125833948024603,376417734772625,1102878148698235

%N Number of partitions of n into parts of 23 kinds.

%C a(n) is Euler transform of A010862. - _Alois P. Heinz_, Oct 17 2008

%C Convolved with A000041 = A006922. - _Gary W. Adamson_, Jun 09 2009

%H Alois P. Heinz, <a href="/A023021/b023021.txt">Table of n, a(n) for n = 0..1000</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%H <a href="/index/Pro#1mxtok">Index entries for expansions of Product_{k >= 1} (1-x^k)^m</a>

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

%F a(0) = 1, a(n) = (23/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Mar 27 2017

%p 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

%t CoefficientList[1/QPochhammer[q]^23 + O[q]^30, q] (* _Jean-Fran├žois Alcover_, Dec 03 2015 *)

%o (PARI) Vec(1/eta(x)^23 + O(x^30)) \\ _Indranil Ghosh_, Mar 27 2017

%Y Cf. 23rd column of A144064. - _Alois P. Heinz_, Oct 17 2008

%Y Cf. A006922, A000041. - _Gary W. Adamson_, Jun 09 2009

%K nonn

%O 0,2

%A _David W. Wilson_

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Last modified October 20 17:42 EDT 2019. Contains 328268 sequences. (Running on oeis4.)