A234528 a(n) = binomial(10*n+5,n)/(2*n+1).

1, 5, 60, 935, 16555, 316251, 6353760, 132321990, 2830853610, 61841702065, 1373736123760, 30935736733230, 704631080073635, 16204866668942000, 375762274309378440, 8775795659568727020, 206241872189050376550, 4873761343609509542490, 115739658699097625728900, 2760617469405074988723180

Offset

0,2

Comments

Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), where p=10, r=5.

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=5.

a(n) ~ 4^(5*n+2) * 5^(10*n+11/2) / (3^(18*n+11) * n^(3/2) * sqrt(Pi)). - Amiram Eldar, Sep 15 2025

Mathematica

Table[Binomial[10 n + 5, n]/(2 n + 1), {n, 0, 30}] (* Vincenzo Librandi, Dec 28 2013 *)

Prog

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

Crossrefs

Cf. A000108, A059968, A234525, A234526, A234527, A234529, A234570, A234571, A234573, A229963.

Sequence in context: A370445 A093885 A192948 * A380213 A277300 A156125

Adjacent sequences: A234525 A234526 A234527 * A234529 A234530 A234531

Keyword

nonn

Author

Tim Fulford, Dec 27 2013

Status

approved