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A233908 10*binomial(7*n+10,n)/(7*n+10).

%I A233908 #22 Sep 08 2022 08:46:06
%S A233908 1,10,115,1450,19425,271502,3915100,57821940,870238200,13298907050,
%T A233908 205811513765,3218995093860,50802419972395,808016193159000,
%U A233908 12938696992921000,208419656266988904,3374960506795660365,54907659530154222000,897060906625956765000
%N A233908 10*binomial(7*n+10,n)/(7*n+10).
%C A233908 Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=7, r=10.
%H A233908 Vincenzo Librandi, <a href="/A233908/b233908.txt">Table of n, a(n) for n = 0..200</a>
%H A233908 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 A233908 Thomas A. Dowling, <a href="http://www.mhhe.com/math/advmath/rosen/r5/instructor/applications/ch07.pdf">Catalan Numbers Chapter 7</a>
%H A233908 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 A233908 Wikipedia, <a href="http://en.wikipedia.org/wiki/Fuss%E2%80%93Catalan_number">Fuss-Catalan number</a>
%F A233908 72*n*(6*n+5)*(3*n+5)*(2*n+3)*(3*n+4)*(6*n+7)*a(n) -7*(7*n+4)*(7*n+8)*(7*n+5)*(7*n+9)*(7*n+6)*(7*n+3)*a(n-1)=0. - _R. J. Mathar_, Dec 22 2013
%F A233908 G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=7, r=10.
%t A233908 Table[10 Binomial[7 n + 10, n]/(7 n + 10), {n, 0, 40}] (* _Vincenzo Librandi_, Dec 23 2013 *)
%o A233908 (PARI) a(n) = 10*binomial(7*n+10,n)/(7*n+10);
%o A233908 (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(7/10))^10+x*O(x^n)); polcoeff(B, n)}
%o A233908 (Magma) [10*Binomial(7*n+10, n)/(7*n+10): n in [0..30]]; // _Vincenzo Librandi_, Dec 23 2013
%Y A233908 Cf. A000108, A002296, A233832 - A233835, A143547, A130565, A233907.
%K A233908 nonn
%O A233908 0,2
%A A233908 _Tim Fulford_, Dec 17 2013