%I #47 Feb 06 2018 09:18:58
%S 1,7,35,140,490,1547,4522,12405,32305,80465,192899,447146,1006145,
%T 2204475,4715510,9869132,20247710,40786690,80782800,157510780,
%U 302666903,573720808,1073720305,1985506775,3630307835,6567206471,11760658378,20860415590,36665885170,63891010155,110415782785,189320804673,322174588225
%N Number of partitions of n into parts of 7 kinds.
%C a(n) is Euler transform of A010727. - _Alois P. Heinz_, Oct 17 2008
%H Seiichi Manyama, <a href="/A023006/b023006.txt">Table of n, a(n) for n = 0..1000</a> (first 201 terms from Vincenzo Librandi)
%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 G.f.: Product_{m>=1} 1/(1-x^m)^7.
%F a(n) ~ 49 * exp(Pi * sqrt(14*n/3)) / (576 * sqrt(2) * n^(5/2)). - _Vaclav Kotesovec_, Feb 28 2015
%F a(0) = 1, a(n) = (7/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Mar 26 2017
%F G.f.: exp(7*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*7, 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)^7,{k,1,nmax}],{x,0,nmax}],x] (* _Vaclav Kotesovec_, Feb 28 2015 *)
%o (PARI) Vec(1/eta('x+O('x^66))^7) /* _Joerg Arndt_, Jul 30 2011 */
%Y Cf. 7th column of A144064. - _Alois P. Heinz_, Oct 17 2008
%K nonn
%O 0,2
%A _David W. Wilson_