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A230547
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a(n) = 3*binomial(3*n+9, n)/(n+3).
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3
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1, 9, 63, 408, 2565, 15939, 98670, 610740, 3786588, 23535820, 146710476, 917263152, 5752004349, 36174046743, 228124619100, 1442387942520, 9142452842985, 58083251802345, 369816259792035, 2359448984037600
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OFFSET
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0,2
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COMMENTS
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Fuss-Catalan sequence is a(n,p,r) = r*binomial(np+r,n)/(np+r), this is the case p=3, r=9.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..200
J-C. Aval, Multivariate Fuss-Catalan Numbers, arXiv:0711.0906 [math.CO], 2007; 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.
Emanuele Munarini, Shifting Property for Riordan, Sheffer and Connection Constants Matrices, Journal of Integer Sequences, Vol. 20 (2017), Article 17.8.2.
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FORMULA
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G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, here p=3, r=9.
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MATHEMATICA
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Table[9 Binomial[3 n + 9, n]/(3 n + 9), {n, 0, 30}]
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PROG
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(PARI) a(n) = 9*binomial(3*n+9, n)/(3*n+9);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(3/9))^9+x*O(x^n)); polcoeff(B, n)}
(Magma) [9*Binomial(3*n+9, n)/(3*n+9): n in [0..30]];
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CROSSREFS
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Cf. A000108, A001764, A006013, A006629, A102893, A006630, A102594, A006631, A233657.
Sequence in context: A022733 A111997 A016137 * A339786 A201885 A225964
Adjacent sequences: A230544 A230545 A230546 * A230548 A230549 A230550
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KEYWORD
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nonn
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AUTHOR
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Tim Fulford, Oct 23 2013
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STATUS
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approved
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