A233830 a(n) = 5*binomial(6*n+10,n)/(3*n+5).

1, 10, 105, 1170, 13640, 164502, 2036265, 25727800, 330482295, 4303216330, 56672074888, 753573733050, 10103474312100, 136435868978220, 1854009194816745, 25333847134998864, 347880174736462550, 4798137522234602700, 66441427922465470095, 923346006310186106010, 12873823246049001482400

Offset

0,2

Comments

Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=6, r=10.

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, here p=6, r=10.

From Ilya Gutkovskiy, Sep 14 2018: (Start)

E.g.f.: 6F6(5/3,11/6,2,13/6,7/3,5/2; 1,11/5,12/5,13/5,14/5,3; 46656*x/3125).

a(n) ~ 3^(6*n+19/2)*4^(3*n+5)/(sqrt(Pi)*5^(5*n+19/2)*n^(3/2)). (End)

Mathematica

Table[5 Binomial[6 n + 10, n]/(3 n + 5), {n, 0, 30}]

Prog

(PARI) a(n) = 5*binomial(6*n+10, n)/(3*n+5);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(3/5))^10+x*O(x^n)); polcoeff(B, n)}
(Magma) [5*Binomial(6*n+10, n)/(3*n+5): n in [0..30]];

Crossrefs

Cf. A000108, A002295, A212071, A212072, A212073, A130564, A233743, A233827, A233829.

Sequence in context: A004343 A163166 A068767 * A046715 A145713 A123512

Adjacent sequences: A233827 A233828 A233829 * A233831 A233832 A233833

Keyword

nonn

Author

Tim Fulford, Dec 16 2013

Status

approved