A233669 a(n) = 7*binomial(5*n+7, n)/(5*n+7).

1, 7, 56, 490, 4550, 44051, 439824, 4496388, 46834095, 495260150, 5303177880, 57385471962, 626548297648, 6893781417320, 76362138282400, 850867975145160, 9530515916642385, 107249427630005661, 1211964598880990640, 13747501038498835300

Offset: 0

Author

Tim Fulford, Dec 14 2013

Keywords

• nonn
• easy

Comments

Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=5, r=7.

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.

Crossrefs

Cf. A000108, A002294, A118969, A143546, A118971, A233668, A233736, A233737, A233738.

Programs

Magma

[7*Binomial(5*n+7,n)/(5*n+7): n in [0..30]];

Mathematica

Table[7 Binomial[5 n + 7, n]/(5 n + 7), {n, 0, 30}]

PARI

a(n) = 7*binomial(5*n+7,n)/(5*n+7);

PARI

{a(n)=local(B=1); for(i=0, n, B=(1+x*B^(5/7))^7+x*O(x^n)); polcoeff(B, n)}

Formula

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, here p=5, r=7.

From Ilya Gutkovskiy, Sep 14 2018: (Start)

E.g.f.: 4F4(7/5,8/5,9/5,11/5; 1,9/4,5/2,11/4; 3125*x/256).

a(n) ~ 7*5^(5*n+13/2)/(sqrt(Pi)*2^(8*n+31/2)*n^(3/2)). (End)