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A233834 a(n) = 5*binomial(7*n+5,n)/(7*n+5). 10
1, 5, 45, 500, 6200, 82251, 1142295, 16398200, 241379325, 3623534200, 55262073757, 853814730600, 13335836817420, 210225027967325, 3340362288091500, 53443628421286320, 860246972339613855, 13921016318025200505, 226352372251889455000, 3696160728052814340000 (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 = 5.

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: A(x) = {1 + x*A(x)^(p/r)}^r, where p = 7, r = 5.

O.g.f. A(x) = 1/x * series reversion (x/C(x)^5), where C(x) is the o.g.f. for the Catalan numbers A000108. A(x)^(1/5) is the o.g.f. for A002296. - Peter Bala, Oct 14 2015

MATHEMATICA

Table[5 Binomial[7 n + 5, n]/(7 n + 5), {n, 0, 30}]

PROG

(PARI) a(n) = 5*binomial(7*n+5, n)/(7*n+5);

(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(7/5))^5+x*O(x^n)); polcoeff(B, n)}

(MAGMA) [5*Binomial(7*n+5, n)/(7*n+5): n in [0..30]];

CROSSREFS

Cf. A000108, A002296, A233832, A233833, A143547, A130565, A233835, A233907, A233908, A002296, A069271, A118970, A212073, A234465, A234510, A234571, A235339.

Sequence in context: A195188 A232730 A151831 * A188267 A133305 A316705

Adjacent sequences:  A233831 A233832 A233833 * A233835 A233836 A233837

KEYWORD

nonn,easy

AUTHOR

Tim Fulford, Dec 16 2013

STATUS

approved

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Last modified April 12 00:12 EDT 2021. Contains 342910 sequences. (Running on oeis4.)