cp's OEIS Frontend

A233658 7*binomial(4*n + 7, n)/(4*n + 7).

%I A233658 #24 Nov 22 2024 08:39:46
%S A233658 1,7,49,357,2695,20930,166257,1344904,11042724,91801255,771201431,
%T A233658 6536904290,55838330730,480197194260,4154140621425,36126361733616,
%U A233658 315647802951628,2769544822393356,24392874398953060,215582307059144025,1911286446370861455,16993580092566979770,151491588134469616215
%N A233658 7*binomial(4*n + 7, n)/(4*n + 7).
%C A233658 Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=4, r=7.
%H A233658 Vincenzo Librandi, <a href="/A233658/b233658.txt">Table of n, a(n) for n = 0..200</a>
%H A233658 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 A233658 Thomas A. Dowling, <a href="http://www.mhhe.com/math/advmath/rosen/r5/instructor/applications/ch07.pdf">Catalan Numbers Chapter 7</a>
%H A233658 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 A233658 G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=4, r=7.
%F A233658 D-finite with recurrence 3*(3*n+5)*(3*n+7)*(n+2)*a(n) -(n+1)*(661*n^2+1301*n+558)*a(n-1) +120*(4*n+1)*(2*n+1)*(4*n-1)*a(n-2)=0. - _R. J. Mathar_, Nov 22 2024
%F A233658 D-finite with recurrence 3*n*(3*n+5)*(3*n+7)*(n+2)*a(n) -8*(4*n+5)*(2*n+3)*(4*n+3)*(n+1)*a(n-1)=0. - _R. J. Mathar_, Nov 22 2024
%t A233658 Table[7 Binomial[4 n + 7, n]/(4 n + 7), {n, 0, 30}]
%o A233658 (PARI) a(n) = 7*binomial(4*n+7,n)/(4*n+7);
%o A233658 (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(4/7))^7+x*O(x^n)); polcoeff(B, n)}
%o A233658 (Magma) [7*Binomial(4*n+7,n)/(4*n+7): n in [0..30]];
%Y A233658 Cf. A000108, A002293, A069271, A006632, A196678, A006633, A233666, A006634, A233667.
%K A233658 nonn,easy
%O A233658 0,2
%A A233658 _Tim Fulford_, Dec 14 2013