login
5*binomial(8*n+5, n)/(8*n+5).
9

%I #16 Sep 08 2022 08:46:06

%S 1,5,50,630,8925,135751,2165800,35759900,605902440,10475490875,

%T 184068392508,3277575482090,59012418601500,1072549882307925,

%U 19651558477204200,362592313327737592,6731396321743423000,125645122201355505000,2356570385677427920770

%N 5*binomial(8*n+5, n)/(8*n+5).

%C Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=8, r=5.

%H Vincenzo Librandi, <a href="/A234464/b234464.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.

%F G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=8, r=5.

%t Table[5 Binomial[8 n + 5, n]/(8 n + 5), {n, 0, 40}] (* _Vincenzo Librandi_, Dec 26 2013 *)

%o (PARI) a(n) = 5*binomial(8*n+5,n)/(8*n+5);

%o (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(8/5))^5+x*O(x^n)); polcoeff(B, n)}

%o (Magma) [5*Binomial(8*n+5, n)/(8*n+5): n in [0..30]]; // _Vincenzo Librandi_, Dec 26 2012

%Y Cf. A000108, A007556, A234461, A234462, A234463, A234465, A234466, A234467, A230390.

%K nonn

%O 0,2

%A _Tim Fulford_, Dec 26 2013