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A233667
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a(n) = 5*binomial(4*n+10,n)/(2*n+5).
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5
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1, 10, 85, 700, 5750, 47502, 395560, 3321120, 28102425, 239503550, 2054455634, 17726454200, 153757722300, 1340045361750, 11729338225200, 103068670351552, 908923976461140, 8041606944709800, 71359997110169625, 634978885837495500, 5664526697522326590
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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=4, r=10.
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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=4, r=10.
E.g.f.: 4F4(5/2,11/4,3,13/4; 1,11/3,4,13/3; 256*x/27).
a(n) ~ 5*2^(8*n+39/2)/(sqrt(Pi)*3^(3*n+21/2)*n^(3/2)). (End)
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MATHEMATICA
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Table[5 Binomial[4 n + 10, n]/(2 n + 5), {n, 0, 30}]
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PROG
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(PARI) a(n) = 5*binomial(4*n+10, n)/(2*n+5);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(2/5))^10+x*O(x^n)); polcoeff(B, n)}
(Magma) [5*Binomial(4*n+10, n)/(2*n+5): n in [0..30]];
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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