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A233738 2*binomial(5*n+10, n)/(n+2).

%I A233738 #30 Nov 22 2024 08:50:47
%S A233738 1,10,95,920,9135,92752,959595,10084360,107375730,1156073100,
%T A233738 12565671261,137702922560,1519842008360,16880051620320,
%U A233738 188519028884675,2115822959020080,23851913523156675,269958280013904870,3066451080298820830,34946186787944832400
%N A233738 2*binomial(5*n+10, n)/(n+2).
%C A233738 Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=5, r=10.
%H A233738 Vincenzo Librandi, <a href="/A233738/b233738.txt">Table of n, a(n) for n = 0..200</a>
%H A233738 J-C. Aval, <a href="http://arxiv.org/abs/0711.0906">Multivariate Fuss-Catalan Numbers</a>, arXiv:0711.0906 [math.CO], 2007.
%H A233738 J-C. Aval, <a href="http://dx.doi.org/10.1016/j.disc.2007.08.100">Multivariate Fuss-Catalan Numbers</a>, Discrete Math., 308 (2008), 4660-4669.
%H A233738 Thomas A. Dowling, <a href="http://www.mhhe.com/math/advmath/rosen/r5/instructor/applications/ch07.pdf">Catalan Numbers Chapter 7</a>
%H A233738 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 A233738 G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=5, r=10.
%F A233738 a(n) = 2*A004344(n)/(n+2). - _Wesley Ivan Hurt_, Sep 07 2014
%F A233738 G.f.: hypergeom([2, 11/5, 12/5, 13/5, 14/5], [11/4, 3, 13/4, 7/2], (3125/256)*x). - _Robert Israel_, Sep 07 2014
%F A233738 D-finite with recurrence 8*(2*n+5)*(4*n+7)*(n+2)*(4*n+9)*a(n) -(n+1)*(13877*n^3+45630*n^2+46579*n+14034)*a(n-1) +210*(5*n+1)*(5*n+2)*(5*n+3)*(5*n+4)*a(n-2)=0. - _R. J. Mathar_, Nov 22 2024
%F A233738 D-finite with recurrence 8*n*(2*n+5)*(4*n+7)*(n+2)*(4*n+9)*a(n) -5*(5*n+6)*(5*n+7)*(5*n+8)*(5*n+9)*(n+1)*a(n-1)=0. - _R. J. Mathar_, Nov 22 2024
%p A233738 A233738:=n->2*binomial(5*n+10,n)/(n+2): seq(A233738(n), n=0..30); # _Wesley Ivan Hurt_, Sep 07 2014
%t A233738 Table[2 Binomial[5 n + 10, n]/(n + 2), {n, 0, 40}] (* _Vincenzo Librandi_, Dec 16 2013 *)
%o A233738 (PARI) a(n) = 2*binomial(5*n+10,n)/(n+2);
%o A233738 (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(1/2))^10+x*O(x^n)); polcoeff(B, n)}
%o A233738 (Magma) [2*Binomial(5*n+10, n)/(n+2): n in [0..30]]; // _Vincenzo Librandi_, Dec 16 2013
%Y A233738 Cf. A000108, A002294, A004344, A118969, A118971, A143546, A233668, A233669, A233736, A233737.
%K A233738 nonn,easy
%O A233738 0,2
%A A233738 _Tim Fulford_, Dec 15 2013