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A233658
7*binomial(4*n + 7, n)/(4*n + 7).
5
1, 7, 49, 357, 2695, 20930, 166257, 1344904, 11042724, 91801255, 771201431, 6536904290, 55838330730, 480197194260, 4154140621425, 36126361733616, 315647802951628, 2769544822393356, 24392874398953060, 215582307059144025, 1911286446370861455, 16993580092566979770, 151491588134469616215
OFFSET
0,2
COMMENTS
Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=4, r=7.
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=4, r=7.
MATHEMATICA
Table[7 Binomial[4 n + 7, n]/(4 n + 7), {n, 0, 30}]
PROG
(PARI) a(n) = 7*binomial(4*n+7, n)/(4*n+7);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(4/7))^7+x*O(x^n)); polcoeff(B, n)}
(Magma) [7*Binomial(4*n+7, n)/(4*n+7): n in [0..30]];
KEYWORD
nonn,easy
AUTHOR
Tim Fulford, Dec 14 2013
STATUS
approved