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A233834 a(n) = 5*binomial(7*n+5,n)/(7*n+5).

%I A233834 #22 Sep 08 2022 08:46:06
%S A233834 1,5,45,500,6200,82251,1142295,16398200,241379325,3623534200,
%T A233834 55262073757,853814730600,13335836817420,210225027967325,
%U A233834 3340362288091500,53443628421286320,860246972339613855,13921016318025200505,226352372251889455000,3696160728052814340000
%N A233834 a(n) = 5*binomial(7*n+5,n)/(7*n+5).
%C A233834 Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p = 7, r = 5.
%H A233834 Vincenzo Librandi, <a href="/A233834/b233834.txt">Table of n, a(n) for n = 0..200</a>
%H A233834 J-C. Aval, <a href="http://arxiv.org/pdf/0711.0906v1.pdf">Multivariate Fuss-Catalan Numbers</a>, arXiv:0711.0906v1, Discrete Math., 308 (2008), 4660-4669.
%H A233834 Thomas A. Dowling, <a href="http://www.mhhe.com/math/advmath/rosen/r5/instructor/applications/ch07.pdf">Catalan Numbers Chapter 7</a>
%H A233834 Wojciech Mlotkowski, <a href="http://www.math.uiuc.edu/documenta/vol-15/28.pdf">Fuss-Catalan Numbers in Noncommutative Probability</a>, Docum. Mathm. 15: 939-955.
%H A233834 Wikipedia, <a href="https://en.wikipedia.org/wiki/Fuss-Catalan_number">Fuss-Catalan number</a>
%F A233834 G.f. satisfies: A(x) = {1 + x*A(x)^(p/r)}^r, where p = 7, r = 5.
%F A233834 O.g.f. A(x) = 1/x * series reversion (x/C(x)^5), where C(x) is the o.g.f. for the Catalan numbers A000108. A(x)^(1/5) is the o.g.f. for A002296. - _Peter Bala_, Oct 14 2015
%t A233834 Table[5 Binomial[7 n + 5, n]/(7 n + 5), {n, 0, 30}]
%o A233834 (PARI) a(n) = 5*binomial(7*n+5,n)/(7*n+5);
%o A233834 (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(7/5))^5+x*O(x^n)); polcoeff(B, n)}
%o A233834 (Magma) [5*Binomial(7*n+5, n)/(7*n+5): n in [0..30]];
%Y A233834 Cf. A000108, A002296, A233832, A233833, A143547, A130565, A233835, A233907, A233908, A002296, A069271, A118970, A212073, A234465, A234510, A234571, A235339.
%K A233834 nonn,easy
%O A233834 0,2
%A A233834 _Tim Fulford_, Dec 16 2013