cp's OEIS Frontend

A023010 Number of partitions of n into parts of 11 kinds.

%I A023010 #26 Feb 06 2018 09:19:17
%S A023010 1,11,77,418,1925,7854,29183,100529,325193,997150,2919411,8207563,
%T A023010 22259237,58454165,149104450,370410700,898202998,2130141651,
%U A023010 4949034937,11281187225,25262712629,55641782779,120661583781,257862888360,543532730675,1130864017283
%N A023010 Number of partitions of n into parts of 11 kinds.
%C A023010 a(n) is Euler transform of A010850. - _Alois P. Heinz_, Oct 17 2008
%H A023010 Alois P. Heinz, <a href="/A023010/b023010.txt">Table of n, a(n) for n = 0..1000</a>
%H A023010 <a href="/index/Pro#1mxtok">Index entries for expansions of Product_{k >= 1} (1-x^k)^m</a>
%H A023010 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A023010 G.f.: Product_{m>=1} 1/(1-x^m)^11.
%F A023010 a(n) ~ 1331 * exp(Pi * sqrt(22*n/3)) / (2^(19/2) * 27 * n^(7/2)). - _Vaclav Kotesovec_, Feb 28 2015
%F A023010 a(0) = 1, a(n) = (11/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Mar 27 2017
%F A023010 G.f.: exp(11*Sum_{k>=1} x^k/(k*(1 - x^k))). - _Ilya Gutkovskiy_, Feb 06 2018
%p A023010 with(numtheory): a:= proc(n) option remember; `if`(n=0, 1, add(add(d*11, d=divisors(j)) *a(n-j), j=1..n)/n) end: seq(a(n), n=0..40); # _Alois P. Heinz_, Oct 17 2008
%t A023010 nmax=50; CoefficientList[Series[Product[1/(1-x^k)^11,{k,1,nmax}],{x,0,nmax}],x] (* _Vaclav Kotesovec_, Feb 28 2015 *)
%t A023010 CoefficientList[Series[1/QPochhammer[x]^11, {x, 0, 30}], x] (* _Indranil Ghosh_, Mar 27 2017 *)
%o A023010 (PARI) Vec(1/eta(x)^11 + O(x^30)) \\ _Indranil Ghosh_, Mar 27 2017
%Y A023010 Cf. 11th column of A144064. - _Alois P. Heinz_, Oct 17 2008
%K A023010 nonn
%O A023010 0,2
%A A023010 _David W. Wilson_