cp's OEIS Frontend

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

%I A023021 #36 Jun 28 2025 08:47:18
%S A023021 1,23,299,2852,22126,147407,871838,4680845,23177583,107100903,
%T A023021 466066181,1923780950,7576060505,28601630657,103928814438,
%U A023021 364712523658,1239637963457,4091266414235,13139808783725,41145568478988,125833948024603,376417734772625,1102878148698235
%N A023021 Number of partitions of n into parts of 23 kinds.
%C A023021 a(n) is Euler transform of A010862. - _Alois P. Heinz_, Oct 17 2008
%C A023021 Convolved with A000041 = A006922. - _Gary W. Adamson_, Jun 09 2009
%H A023021 Alois P. Heinz, <a href="/A023021/b023021.txt">Table of n, a(n) for n = 0..1000</a>
%H A023021 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A023021 <a href="/index/Pro#1mxtok">Index entries for expansions of Product_{k >= 1} (1-x^k)^m</a>
%F A023021 G.f.: Product_{m>=1} 1/(1-x^m)^23.
%F A023021 a(0) = 1, a(n) = (23/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Mar 27 2017
%F A023021 a(n) ~ m^((m+1)/4) * exp(Pi*sqrt(2*m*n/3)) / (2^((3*m+5)/4) * 3^((m+1)/4) * n^((m+3)/4)) * (1 - ((9+Pi^2)*m^2+36*m+27) / (24*Pi*sqrt(6*m*n))), set m = 23. - _Vaclav Kotesovec_, Jun 28 2025
%p A023021 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 A023021 CoefficientList[1/QPochhammer[q]^23 + O[q]^30, q] (* _Jean-François Alcover_, Dec 03 2015 *)
%o A023021 (PARI) Vec(1/eta(x)^23 + O(x^30)) \\ _Indranil Ghosh_, Mar 27 2017
%Y A023021 Cf. 23rd column of A144064. - _Alois P. Heinz_, Oct 17 2008
%Y A023021 Cf. A006922, A000041. - _Gary W. Adamson_, Jun 09 2009
%K A023021 nonn
%O A023021 0,2
%A A023021 _David W. Wilson_