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A234507 4*binomial(9*n+4,n)/(9*n+4). 8
1, 4, 42, 580, 9139, 155664, 2791404, 51919296, 992414925, 19375620264, 384734333698, 7745767624560, 157746595917027, 3243956787596560, 67267249849483200, 1404952651131292800, 29529506061314207361, 624113938377564174540, 13256095235994257535900, 282803564653982441429256, 6057302574889055180495805 (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=9, r=4.

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=9, r=4.

MATHEMATICA

Table[4 Binomial[9 n + 4, n]/(9 n + 4), {n, 0, 30}]

PROG

(PARI) a(n) = 4*binomial(9*n+4, n)/(9*n+4);

(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(9/1))^1+x*O(x^n)); polcoeff(B, n)}

(MAGMA) [1*Binomial(9*n+1, n)/(9*n+1): n in [0..30]];

CROSSREFS

Cf. A000108, A143554, A234505, A234506, A234508, A234509, A234510, A234513, A232265.

Sequence in context: A249928 A156440 A151453 * A153854 A216080 A137645

Adjacent sequences:  A234504 A234505 A234506 * A234508 A234509 A234510

KEYWORD

nonn

AUTHOR

Tim Fulford, Dec 27 2013

STATUS

approved

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Last modified July 13 15:18 EDT 2020. Contains 335688 sequences. (Running on oeis4.)