PROG
(MAGMAMagma) [1*Binomial(9*n+1, n)/(9*n+1): n in [0..30]];
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(MAGMAMagma) [1*Binomial(9*n+1, n)/(9*n+1): n in [0..30]];
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Vincenzo Librandi, <a href="/A234507/b234507.txt">Table of n, a(n) for n = 0..200</a>
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Fuss-Catalan sequence is a(n,p,r,s) = sr*binomial(nrnp+s,r,n)/(nrnp+s), this is the case s=4, r), where p=9, r=4.
J-C. Aval, <a href="http://www.labriarxiv.fr/persoorg/avalpdf/b50711.0906v1 Multivariate Fuss-Catalan Numbers</a>, arXiv:0711.0906v1, Discrete Math., 308 (2008), 4660-4669.
Wojciech Mlotkowski, <a href="http://www.math.uiuc.edu/documenta/vol-15/28.pdf">Fuss-Catalan Numbers in Noncommutative Probability</a>, Docum. Mathm. 15: 939-955.
G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=9, r=4.
Table[4 Binomial[9 n + 4, n]/(9 n + 4), {n, 0, 30}]
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(9/1))^1+x*O(x^n)); polcoeff(B, n)}
(MAGMA) [1*Binomial(9*n+1, n)/(9*n+1): n in [0..30]];
nonn,changednew
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4*binomial(9*n+4,n)/(9*n+4).
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