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%I #24 Sep 08 2022 08:46:06
%S 1,7,84,1232,20090,349860,6371764,119877472,2311664355,45448324110,
%T 907580289616,18358110017520,375353605696524,7744997102466932,
%U 161070300819384000,3372697621463787456,71046594621639707245,1504569659175026591805
%N a(n) = 7*binomial(9*n+7,n)/(9*n+7).
%C Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), where p = 9, r = 7.
%H Vincenzo Librandi, <a href="/A234510/b234510.txt">Table of n, a(n) for n = 0..200</a>
%H 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 Thomas A. Dowling, <a href="http://www.mhhe.com/math/advmath/rosen/r5/instructor/applications/ch07.pdf">Catalan Numbers Chapter 7</a>
%H 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 Wikipedia, <a href="https://en.wikipedia.org/wiki/Fuss-Catalan_number">Fuss-Catalan number</a>
%F G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p = 9, r = 7.
%F O.g.f. A(x) = 1/x * series reversion (x/C(x)^7), where C(x) is the o.g.f. for the Catalan numbers A000108. A(x)^(1/7) is the o.g.f. for A062994. - _Peter Bala_, Oct 14 2015
%t Table[7 Binomial[9 n + 7, n]/(9 n + 7), {n, 0, 40}] (* _Vincenzo Librandi_, Dec 27 2013 *)
%o (PARI) a(n) = 7*binomial(9*n+7,n)/(9*n+7);
%o (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(9/7))^7+x*O(x^n)); polcoeff(B, n)}
%o (Magma) [7*Binomial(9*n+7, n)/(9*n+7): n in [0..30]]; // _Vincenzo Librandi_, Dec 27 2013
%Y Cf. A000108, A143554, A234505, A234506, A234507, A234508, A234509, A234513, A232265, A062994, A069271, A118970, A212073, A233834, A234465, A234571, A235339.
%K nonn,easy
%O 0,2
%A _Tim Fulford_, Dec 27 2013
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