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A234464 5*binomial(8*n+5, n)/(8*n+5). 9
1, 5, 50, 630, 8925, 135751, 2165800, 35759900, 605902440, 10475490875, 184068392508, 3277575482090, 59012418601500, 1072549882307925, 19651558477204200, 362592313327737592, 6731396321743423000, 125645122201355505000, 2356570385677427920770 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=8, r=5.

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, where p=8, r=5.

MATHEMATICA

Table[5 Binomial[8 n + 5, n]/(8 n + 5), {n, 0, 40}] (* Vincenzo Librandi, Dec 26 2013 *)

PROG

(PARI) a(n) = 5*binomial(8*n+5, n)/(8*n+5);

(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(8/5))^5+x*O(x^n)); polcoeff(B, n)}

(MAGMA) [5*Binomial(8*n+5, n)/(8*n+5): n in [0..30]]; // Vincenzo Librandi, Dec 26 2012

CROSSREFS

Cf. A000108, A007556, A234461, A234462, A234463, A234465, A234466, A234467, A230390.

Sequence in context: A237020 A156058 A232997 * A047736 A185272 A141316

Adjacent sequences:  A234461 A234462 A234463 * A234465 A234466 A234467

KEYWORD

nonn

AUTHOR

Tim Fulford, Dec 26 2013

STATUS

approved

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Last modified October 23 23:51 EDT 2019. Contains 328379 sequences. (Running on oeis4.)