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 A233668 a(n) = 6*binomial(5*n + 6,n)/(5*n + 6). 11
 1, 6, 45, 380, 3450, 32886, 324632, 3290040, 34034715, 357919100, 3815041230, 41124015036, 447534498320, 4910258796240, 54257308779600, 603260892430960, 6744185681876505, 75764901779438850, 854867886710698755, 9683529727259434200 (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); this is the case p = 5, r = 6. REFERENCES C. H. Pah, M. R. Wahiddin, Combinatorial Interpretation of Raney Numbers and Tree Enumerations, Open Journal of Discrete Mathematics, 2015, 5, 1-9; http://www.scirp.org/journal/ojdm; http://dx.doi.org/10.4236/ojdm.2015.51001 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, here p = 5, r = 6. From _Peter Bala, Oct 16 2015: (Start) O.g.f. A(x) = 1/x * series reversion (x*C(-x)^6), 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)^(1/6) is the o.g.f. for A002294. (End) MATHEMATICA Table[6 Binomial[5 n + 6, n]/(5 n + 6), {n, 0, 30}] PROG (PARI) a(n) = 6*binomial(5*n+6, n)/(5*n+6); (PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(5/6))^6+x*O(x^n)); polcoeff(B, n)} (Magma) [6*Binomial(5*n+6, n)/(5*n+6): n in [0..30]]; CROSSREFS Cf. A000108, A002294, A118969, A143546, A118971, A233669, A233736, A233737, A233738. Cf. A000245 (k = 3), A006629 (k = 4), A196678 (k = 5), A233743 (k = 7), A233835 (k = 8), A234467 (k = 9), A232265 (k = 10), A229963 (k = 11). Sequence in context: A007194 A025551 A101600 * A243694 A227169 A365184 Adjacent sequences: A233665 A233666 A233667 * A233669 A233670 A233671 KEYWORD nonn,easy AUTHOR Tim Fulford, Dec 14 2013 STATUS approved

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