A235339 a(n) = 9*binomial(11*n+9,n)/(11*n+9).

1, 9, 135, 2460, 49725, 1072197, 24163146, 562311720, 13409091540, 325949656825, 8046743477058, 201198155083200, 5084704634041305, 129673310477725350, 3332952595603387800, 86250038091202771344, 2245329811618166111985, 58761538063393442801940, 1545071600161918242262100

Offset

0,2

Comments

Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p = 11, r = 9.

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.

Wikipedia, Fuss-Catalan number.

Formula

G.f. satisfies: A(x) = (1 + x*A(x)^(p/r))^r, here p = 11, r = 9.

O.g.f.: A(x) = (1/x) * series reversion (x/C(x)^9), where C(x) is the o.g.f. for the Catalan numbers A000108. A(x)^(1/9) is the o.g.f. for A230388. - Peter Bala, Oct 14 2015

a(n) ~ 9 * 11^(11*n+17/2) / (2^(10*n+10) * 5^(10*n+19/2) * n^(3/2) * sqrt(Pi)). - Amiram Eldar, Sep 15 2025

Mathematica

Table[9 Binomial[11 n + 9, n]/(11 n + 9), {n, 0, 30}]

Prog

(PARI) a(n) = 9*binomial(11*n+9, n)/(11*n+9);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(11/9))^9+x*O(x^n)); polcoeff(B, n)}
(Magma) [9*Binomial(11*n+9, n)/(11*n+9): n in [0..30]];

Crossrefs

Cf. A230388, A234868, A234869, A234870, A234871, A234872, A234873, A235338, A235340, A069271, A118970, A212073, A230388, A233834, A234465, A234510, A234571.

Sequence in context: A254282 A385119 A395287 * A306848 A034723 A391557

Adjacent sequences: A235336 A235337 A235338 * A235340 A235341 A235342

Keyword

nonn,easy

Author

Tim Fulford, Jan 06 2014

Status

approved