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A234506
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a(n) = binomial(9*n+3, n)/(3*n+1).
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8
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1, 3, 30, 406, 6327, 107019, 1909908, 35399520, 674842149, 13147742322, 260626484118, 5239783981320, 106585537781775, 2189670831627678, 45366284782209600, 946815917066740800, 19887218367823853937, 420076689292591271325, 8917736795123409615060, 190161017612160607167948, 4071301730663135449185705
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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(n*p + r, n)/(n*p + r), where p=9, r=3.
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LINKS
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FORMULA
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G.f. satisfies: B(x) = {1 + x*B(x)^(p/r)}^r, where p=9, r=3.
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MATHEMATICA
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Table[Binomial[9n+3, n]/(3n+1), {n, 0, 30}]
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PROG
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(PARI) a(n) = binomial(9*n+3, n)/(3*n+1);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^3)^3+x*O(x^n)); polcoeff(B, n)}
(Magma) [Binomial(9*n+3, n)/(3*n+1): n in [0..30]];
(Sage) [binomial(9*n+3, n)/(3*n+1) for n in (0..30)] # G. C. Greubel, Feb 09 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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