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A234571 a(n) = 4*binomial(10*n+8,n)/(5*n+4). 14
1, 8, 108, 1776, 32430, 632016, 12876864, 270964320, 5843355957, 128462407840, 2868356980060, 64869895026144, 1482877843096650, 34207542810153216, 795318309360948240, 18617396126132233920, 438423206616057162258, 10379232525028947311160, 246878659984195222962220 (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), where p = 10, r = 8.

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.

Wikipedia, Fuss-Catalan number

FORMULA

G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p = 10, r = 8.

O.g.f. A(x) = 1/x * series reversion (x/C(x)^8), where C(x) is the o.g.f. for the Catalan numbers A000108. A(x)^(1/8) is the o.g.f. for A059968. - Peter Bala, Oct 14 2015

MATHEMATICA

Table[4 Binomial[10 n + 8, n]/(5 n + 4), {n, 0, 30}]

PROG

(PARI) a(n) = 4*binomial(10*n+8, n)/(5*n+4);

(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(5/4))^8+x*O(x^n)); polcoeff(B, n)}

(Magma) [4*Binomial(10*n+8, n)/(5*n+4): n in [0..30]];

CROSSREFS

Cf. A059968, A234525, A234526, A234527, A234528, A234529, A234570, A234573, A059968, A069271, A118970, A212073, A233834, A234465, A234510, A235339.

Sequence in context: A301446 A272497 A215129 * A120975 A193678 A265277

Adjacent sequences:  A234568 A234569 A234570 * A234572 A234573 A234574

KEYWORD

nonn,easy

AUTHOR

Tim Fulford, Dec 28 2013

STATUS

approved

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Last modified October 1 19:48 EDT 2022. Contains 357172 sequences. (Running on oeis4.)