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A232265 a(n) = 10*binomial(9*n + 10, n)/(9*n + 10). 14
1, 10, 135, 2100, 35475, 632502, 11714745, 223198440, 4346520750, 86128357150, 1731030945644, 35202562937100, 723029038312230, 14976976398326250, 312522428615310000, 6563314391270476752, 138617681440915119975, 2942332729799060033100, 62735156704285184848950 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Fuss-Catalan sequence is a(n,p,r) = r*binomial(n*p + r,n)/(n*p + r), where p = 9, r = 10.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

J-C. Aval, Multivariate Fuss-Catalan Numbers, arXiv:0711.0906 [math.CO], 2007.

J-C. Aval, Multivariate Fuss-Catalan Numbers, 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: A(x) = {1 + x*A(x)^(p/r)}^r, where p = 9, r = 10.

From _Peter Bala, Oct 16 2015: (Start)

O.g.f. A(x) = 1/x * series reversion (x*C(-x)^10), where C(x) = (1 - sqrt(1 - 4*x))/(2*x) is the o.g.f. for the Catalan numbers A000108. See cross-references for other Fuss-Catalan sequences with o.g.f. 1/x * series reversion (x*C(-x)^k), k = 3 through 11.

A(x)^(1/10) is the o.g.f. for A062994. (End)

MATHEMATICA

Table[10 Binomial[9 n + 10, n]/(9 n + 10), {n, 0, 30}]

PROG

(PARI) a(n) = 10*binomial(9*n+10, n)/(9*n+10);

(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(9/10))^10+x*O(x^n)); polcoeff(B, n)}

(MAGMA) [10*Binomial(9*n+10, n)/(9*n+10): n in [0..30]];

CROSSREFS

Cf. A000108, A143554, A234505, A234506, A234507, A234508, A234509, A234510, A234513.

Cf. A062994, A000245 (k = 3), A006629 (k = 4), A196678 (k = 5), A233668 (k = 6), A233743 (k = 7), A233835 (k = 8), A234467 (k = 9), A229963 (k = 11).

Sequence in context: A218440 A048666 A114936 * A095653 A024135 A050408

Adjacent sequences:  A232262 A232263 A232264 * A232266 A232267 A232268

KEYWORD

nonn,easy

AUTHOR

Tim Fulford, Dec 28 2013

STATUS

approved

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Last modified February 21 00:30 EST 2018. Contains 299388 sequences. (Running on oeis4.)