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%I #35 Feb 06 2018 09:19:05
%S 1,8,44,192,726,2464,7704,22528,62337,164560,417140,1020416,2418710,
%T 5573568,12520744,27484160,59068372,124505880,257770964,524871424,
%U 1052316364,2079491744,4053978040,7803219968,14840711765,27907041392,51917588800,95608651776
%N Number of partitions of n into parts of 8 kinds.
%C a(n) is Euler transform of A010731. - _Alois P. Heinz_, Oct 17 2008
%H Seiichi Manyama, <a href="/A023007/b023007.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from Alois P. Heinz)
%H Roland Bacher, P. De La Harpe, <a href="https://hal.archives-ouvertes.fr/hal-01285685/document">Conjugacy growth series of some infinitely generated groups</a>, 2016, hal-01285685v2.
%H P. Nataf, M. Lajkó, A. Wietek, K. Penc, F. Mila, A. M. Läuchli, <a href="https://arxiv.org/abs/1601.00958">Chiral spin liquids in triangular lattice SU (N) fermionic Mott insulators with artificial gauge fields</a>, arXiv preprint arXiv:1601.00958 [cond-mat.quant-gas], 2016.
%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 a(n) ~ exp(4 * Pi * sqrt(n/3)) / (sqrt(2) * 3^(9/4) * n^(11/4)). - _Vaclav Kotesovec_, Feb 28 2015
%F a(0) = 1, a(n) = (8/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Mar 27 2017
%F G.f.: exp(8*Sum_{k>=1} x^k/(k*(1 - x^k))). - _Ilya Gutkovskiy_, Feb 06 2018
%p with(numtheory): a:= proc(n) option remember; `if`(n=0, 1, add(add(d*8, d=divisors(j)) *a(n-j), j=1..n)/n) end: seq(a(n), n=0..40); # _Alois P. Heinz_, Oct 17 2008
%t nmax=50; CoefficientList[Series[Product[1/(1-x^k)^8,{k,1,nmax}],{x,0,nmax}],x] (* _Vaclav Kotesovec_, Feb 28 2015 *)
%Y Cf. 8th column of A144064. - _Alois P. Heinz_, Oct 17 2008
%K nonn
%O 0,2
%A _David W. Wilson_
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