A235338 a(n) = 8*binomial(11*n+8,n)/(11*n+8).

1, 8, 116, 2080, 41650, 892552, 20027112, 464550336, 11050084695, 268070745800, 6607118937848, 164979021222400, 4164615224071926, 106105019316578800, 2724883054841727200, 70462458864489354624, 1833143662625459289495, 47946736471099378970016, 1260058392365059537378800

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=8.

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, here p=11, r=8.

a(n) ~ 11^(11*n+15/2) / (4^(5*n+3) * 5^(10*n+17/2) * n^(3/2) * sqrt(Pi)). - Amiram Eldar, Sep 15 2025

Mathematica

Table[8 Binomial[11 n + 8, n]/(11 n + 8), {n, 0, 30}]

Prog

(PARI) a(n) = 8*binomial(11*n+8, n)/(11*n+8);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(11/8))^8+x*O(x^n)); polcoeff(B, n)}
(Magma) [8*Binomial(11*n+8, n)/(11*n+8): n in [0..30]];

Crossrefs

Cf. A230388, A234868, A234869, A234870, A234871, A234872, A234873, A235339, A235340.

Sequence in context: A240890 A241105 A214695 * A231553 A291077 A056988

Adjacent sequences: A235335 A235336 A235337 * A235339 A235340 A235341

Keyword

nonn

Author

Tim Fulford, Jan 06 2014

Status

approved