cp's OEIS Frontend

A233907 9*binomial(7*n+9, n)/(7*n+9).

%I A233907 #20 Nov 22 2024 08:44:28
%S A233907 1,9,99,1218,16065,222138,3178140,46656324,698868216,10639125640,
%T A233907 164128169205,2560224004884,40314178429707,639948824981928,
%U A233907 10230035192533800,164541833894991240,2660919275605834701,43239781879996449825,705687913212419321800,11561996402992103418000,190100812111989146008641
%N A233907 9*binomial(7*n+9, n)/(7*n+9).
%C A233907 Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=7, r=9.
%H A233907 Vincenzo Librandi, <a href="/A233907/b233907.txt">Table of n, a(n) for n = 0..200</a>
%H A233907 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 A233907 Thomas A. Dowling, <a href="http://www.mhhe.com/math/advmath/rosen/r5/instructor/applications/ch07.pdf">Catalan Numbers Chapter 7</a>
%H A233907 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 A233907 G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=7, r=9.
%F A233907 D-finite with recurrence 72*n*(6*n+5)*(3*n+2)*(2*n+3)*(3*n+4)*(6*n+7)*a(n) -7*(7*n+4)*(7*n+8)*(7*n+5)*(7*n+2)*(7*n+6)*(7*n+3)*a(n-1)=0. - _R. J. Mathar_, Nov 22 2024
%t A233907 Table[9 Binomial[7 n + 9, n]/(7 n + 9), {n, 0, 30}]
%o A233907 (PARI) a(n) = 9*binomial(7*n+9,n)/(7*n+9);
%o A233907 (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(7/9))^9+x*O(x^n)); polcoeff(B, n)}
%o A233907 (Magma) [9*Binomial(7*n+9, n)/(7*n+9): n in [0..30]];
%Y A233907 Cf. A000108, A002296, A233832, A233833, A143547, A233834, A130565, A233835, A233908.
%K A233907 nonn
%O A233907 0,2
%A A233907 _Tim Fulford_, Dec 17 2013