A234527 a(n) = 2*binomial(10*n+4,n)/(5*n+2).

1, 4, 46, 704, 12341, 234260, 4685898, 97274544, 2075959314, 45262862788, 1003884090440, 22577660493024, 513698787408521, 11802947663348800, 273471432969603198, 6382396843322710560, 149902629054480517590, 3540479504783000035464, 84037056533692623898810, 2003582163362033806248576

Offset

0,2

Comments

Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), where p=10, r=4.

Links

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

Jean-Christophe Aval, Multivariate Fuss-Catalan Numbers, Discrete Math., Vol. 308, No. 20 (2008), 4660-4669; arXiv preprint, arXiv:0711.0906 [math.CO], 2007.

Thomas A. Dowling, Catalan Numbers, Chapter 7 of Applications of discrete mathematics, John G. Michaels and Kenneth H. Rosen (eds.), McGraw-Hill, New York, 1991. [Wayback Machine link]

Wojciech Mlotkowski, Fuss-Catalan Numbers in Noncommutative Probability, Docum. Math. 15 (2010), 939-955.

Formula

G.f. satisfies: A(x) = (1 + x*A(x)^(p/r))^r, where p=10, r=4.

a(n) ~ 2^(10*n+5) * 5^(10*n+7/2) / (3^(18*n+9) * n^(3/2) * sqrt(Pi)). - Amiram Eldar, Sep 14 2025

Mathematica

Table[2 Binomial[10 n + 4, n]/(5 n + 2), {n, 0, 30}] (* Vincenzo Librandi, Dec 28 2013 *)

Prog

(PARI) a(n) = 2*binomial(10*n+4, n)/(5*n+2);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(5/2))^4+x*O(x^n)); polcoeff(B, n)}
(Magma) [2*Binomial(10*n+4, n)/(5*n+2): n in [0..30]]; // Vincenzo Librandi, Dec 28 2013

Crossrefs

Cf. A000108, A059968, A234525, A234526, A234528, A234529, A234570, A234571, A234573, A229963.

Sequence in context: A113264 A264717 A318109 * A126739 A383317 A380646

Adjacent sequences: A234524 A234525 A234526 * A234528 A234529 A234530

Keyword

nonn

Author

Tim Fulford, Dec 27 2013

Status

approved