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A233833
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a(n) = 3*binomial(7*n+3, n)/(7*n+3).
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5
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1, 3, 24, 253, 3045, 39627, 543004, 7718340, 112752783, 1682460520, 25533901536, 392912889915, 6116090678334, 96133810101609, 1523687678528400, 24324750346691480, 390786855500604195, 6313161418594235271, 102494297789621214400, 1671366110239940499000
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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=7, 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=7, r=3.
E.g.f.: 6F6(3/7,4/7,5/7,6/7,8/7,9/7; 2/3,5/6,1,7/6,4/3,3/2; 823543*x/46656).
a(n) ~ 7^(7*n+5/2)/(sqrt(Pi)*3^(6*n+5/2)*4^(3*n+2)*n^(3/2)). (End)
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MATHEMATICA
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Table[3 Binomial[7 n + 3, n]/(7 n + 3), {n, 0, 30}]
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PROG
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(PARI) a(n)=3*binomial(7*n+3, n)/(7*n+3);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(7/3))^3+x*O(x^n)); polcoeff(B, n)}
(Magma) [3*Binomial(7*n+3, n)/(7*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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