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%I #34 Feb 06 2018 09:07:32
%S 1,9,54,255,1035,3753,12483,38709,113265,315445,841842,2164185,
%T 5382276,12994290,30543210,70066809,157199805,345552183,745377215,
%U 1579915080,3294664578,6766656315,13700560491,27370137195,53991639855,105242612526,202837976145
%N Number of partitions of n into parts of 9 kinds.
%C a(n) is Euler transform of A010734. - _Alois P. Heinz_, Oct 17 2008
%H Seiichi Manyama, <a href="/A023008/b023008.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from Alois P. Heinz)
%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) ~ 3^(5/2) * exp(Pi * sqrt(6*n)) / (256 * n^3). - _Vaclav Kotesovec_, Feb 28 2015
%F a(0) = 1, a(n) = (9/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Mar 27 2017
%F G.f.: exp(9*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*9, 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)^9,{k,1,nmax}],{x,0,nmax}],x] (* _Vaclav Kotesovec_, Feb 28 2015 *)
%Y Cf. 9th column of A144064. - _Alois P. Heinz_, Oct 17 2008
%K nonn
%O 0,2
%A _David W. Wilson_
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