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A233829
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a(n) = 3*binomial(6*n+9,n)/(2*n+3).
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4
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1, 9, 90, 975, 11160, 132867, 1629012, 20430900, 260907075, 3381098545, 44352058608, 587787511779, 7858257798300, 105855415586550, 1435361957277480, 19576154604317304, 268364706225271110, 3695862686045572350, 51108790709588823150
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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=6, r=9.
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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=6, r=9.
E.g.f.: 5F5(3/2,5/3,11/6,13/6,7/3; 1,11/5,12/5,13/5,14/5; 46656*x/3125).
a(n) ~ 3^(6*n+21/2)*4^(3*n+4)/(sqrt(Pi)*5^(5*n+19/2)*n^(3/2)). (End)
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MATHEMATICA
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Table[3 Binomial[6 n + 9, n]/(2 n + 3), {n, 0, 30}]
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PROG
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(PARI) a(n) = 3*binomial(6*n+9, n)/(2*n+3);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(2/3))^9+x*O(x^n)); polcoeff(B, n)}
(Magma) [3*Binomial(6*n+9, n)/(2*n+3): n in [0..30]];
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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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