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

1, 4, 38, 468, 6545, 98728, 1566040, 25747128, 434824104, 7498246100, 131477423220, 2337053822012, 42016842044268, 762702138530080, 13959382918289880, 257323577200329904, 4773171937236245400, 89028543731246186400, 1668706597425638149302

Offset

0,2

Comments

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

J-C. Aval, Multivariate Fuss-Catalan Numbers, arXiv:0711.0906v1, Discrete Math., 308 (2008), 4660-4669.

Thomas A. Dowling, Catalan Numbers Chapter 7

Wojciech Mlotkowski, Fuss-Catalan Numbers in Noncommutative Probability, Docum. Mathm. 15: 939-955.

Formula

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=8, r=4.

Mathematica

Table[Binomial[8 n + 4, n]/(2 n + 1), {n, 0, 40}] (* Vincenzo Librandi, Dec 26 2013 *)

Prog

(PARI) a(n) = binomial(8*n+4, n)/(2*n+1);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^2)^4+x*O(x^n)); polcoeff(B, n)}
(Magma) [Binomial(8*n+4, n)/(2*n+1): n in [0..30]]; // Vincenzo Librandi, Dec 26 2013

Crossrefs

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

Sequence in context: A220543 A220748 A192947 * A194044 A317605 A263376

Adjacent sequences: A234460 A234461 A234462 * A234464 A234465 A234466

Keyword

nonn

Author

Tim Fulford, Dec 26 2013

Status

approved