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A234463 Binomial(8*n+4,n)/(2*n+1). 9

%I #19 Sep 08 2022 08:46:06

%S 1,4,38,468,6545,98728,1566040,25747128,434824104,7498246100,

%T 131477423220,2337053822012,42016842044268,762702138530080,

%U 13959382918289880,257323577200329904,4773171937236245400,89028543731246186400,1668706597425638149302

%N Binomial(8*n+4,n)/(2*n+1).

%C Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=8, r=4.

%H Vincenzo Librandi, <a href="/A234463/b234463.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=4.

%t Table[Binomial[8 n + 4, n]/(2 n + 1), {n, 0, 40}] (* _Vincenzo Librandi_, Dec 26 2013 *)

%o (PARI) a(n) = binomial(8*n+4,n)/(2*n+1);

%o (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^2)^4+x*O(x^n)); polcoeff(B, n)}

%o (Magma) [Binomial(8*n+4, n)/(2*n+1): n in [0..30]]; // _Vincenzo Librandi_, Dec 26 2013

%Y Cf. A000108, A007556, A234461, A234462, A234464, A234465, A234466, A234467, A230390.

%K nonn

%O 0,2

%A _Tim Fulford_, Dec 26 2013

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Last modified March 28 09:02 EDT 2024. Contains 371237 sequences. (Running on oeis4.)