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A233737
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a(n) = 9*binomial(5*n+9, n)/(5*n+9).
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5
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1, 9, 81, 759, 7371, 73656, 752913, 7838298, 82832706, 886322710, 9583986555, 104568156819, 1149793519368, 12728471356944, 141747219186705, 1586867219265060, 17848735288114995, 201607141031660871, 2285899896222757346, 26008027474874327190, 296840444852078282610, 3397721117411729991960
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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=5, 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, here p=5, r=9.
E.g.f.: 5F5(9/5,2,11/5,12/5,13/5; 1,5/2,11/4,3,13/4; 3125*x/256).
a(n) ~ 9*5^(5*n+17/2)/(sqrt(Pi)*2^(8*n+39/2)*n^(3/2)). (End)
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MATHEMATICA
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Table[9 Binomial[5 n + 9, n]/(5 n + 9), {n, 0, 30}]
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PROG
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(PARI) a(n) = 9*binomial(5*n+9, n)/(5*n+9);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(5/9))^9+x*O(x^n)); polcoeff(B, n)}
(Magma) [9*Binomial(5*n+9, n)/(5*n+9): 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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