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A233907 9*binomial(7*n+9, n)/(7*n+9). 6
1, 9, 99, 1218, 16065, 222138, 3178140, 46656324, 698868216, 10639125640, 164128169205, 2560224004884, 40314178429707, 639948824981928, 10230035192533800, 164541833894991240, 2660919275605834701, 43239781879996449825, 705687913212419321800, 11561996402992103418000, 190100812111989146008641 (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=7, r=9.
LINKS
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=7, r=9.
MATHEMATICA
Table[9 Binomial[7 n + 9, n]/(7 n + 9), {n, 0, 30}]
PROG
(PARI) a(n) = 9*binomial(7*n+9, n)/(7*n+9);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(7/9))^9+x*O(x^n)); polcoeff(B, n)}
(Magma) [9*Binomial(7*n+9, n)/(7*n+9): n in [0..30]];
CROSSREFS
Sequence in context: A264005 A232943 A245927 * A294120 A015685 A051581
KEYWORD
nonn
AUTHOR
Tim Fulford, Dec 17 2013
STATUS
approved

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Last modified May 28 15:56 EDT 2024. Contains 372916 sequences. (Running on oeis4.)