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A234513 8*binomial(9*n+8,n)/(9*n+8). 10

%I

%S 1,8,100,1496,24682,433160,7932196,149846840,2898753715,57135036024,

%T 1143315429776,23166186450680,474347963242860,9799792252101016,

%U 204022381037886400,4276098770070159096,90151561242584838605,1910564646571462338800

%N 8*binomial(9*n+8,n)/(9*n+8).

%C Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), where p=9, r=8.

%H Vincenzo Librandi, <a href="/A234513/b234513.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 Elżbieta Liszewska, Wojciech Młotkowski, <a href="https://arxiv.org/abs/1907.10725">Some relatives of the Catalan sequence</a>, arXiv:1907.10725 [math.CO], 2019.

%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=9, r=8.

%F From _Wolfdieter Lang_, Feb 06 2020: (Start)

%F G.f.: hypergeom([8, 9, ..., 16]/9, [9, 10, ..., 16]/8, (9^9/8^8)*x).

%F E,g,f.: hypergeom([8, 10, 11, ..., 16]/9, [9, 10,..., 16]/8, (9^9/8^8)*x). Cf. _Ilya Gutkovsky_ in A118971. (End)

%t Table[8 Binomial[9 n + 8, n]/(9 n + 8), {n, 0, 30}] (* _Vincenzo Librandi_, Dec 28 2013 *)

%o (PARI) a(n) = 8*binomial(9*n+8,n)/(9*n+8);

%o (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(9/8))^8+x*O(x^n)); polcoeff(B, n)}

%o (MAGMA) [8*Binomial(9*n+8, n)/(9*n+8): n in [0..30]]; // _Vincenzo Librandi_, Dec 28 2013

%Y Cf. A000108, A118971, A143554, A234466, A234505, A234506, A234507, A234508, A234509, A234510, A232265.

%K nonn,easy

%O 0,2

%A _Tim Fulford_, Dec 27 2013

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Last modified July 15 02:31 EDT 2020. Contains 335762 sequences. (Running on oeis4.)