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A233657
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a(n) = 10 * binomial(3*n+10,n)/(3*n+10).
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3
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1, 10, 75, 510, 3325, 21252, 134550, 848250, 5340060, 33622600, 211915132, 1337675430, 8458829925, 53591180360, 340185835500, 2163581913780, 13786238414025, 88004926973250, 562763873596575, 3604713725613000, 23126371951808268, 148594788106641360
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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=3, 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, here p=3, r=10.
+2*n*(n+5)*(2*n+9)*a(n) -3*(3*n+7)*(n+3)*(3*n+8)*a(n-1)=0. - R. J. Mathar, Feb 16 2018
E.g.f.: F([10/3, 11/3, 4], [1, 11/2, 6], 27*x/4), where F is the generalized hypergeometric function. - Stefano Spezia, Oct 08 2019
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MAPLE
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MATHEMATICA
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Table[10 Binomial[3 n + 10, n]/(3 n + 10), {n, 0, 30}]
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PROG
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(PARI) a(n) = 10*binomial(3*n+10, n)/(3*n+10);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(3/10))^10+x*O(x^n)); polcoeff(B, n)}
(Magma) [10*Binomial(3*n+10, n)/(3*n+10): 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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