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A233834
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a(n) = 5*binomial(7*n+5,n)/(7*n+5).
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10
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1, 5, 45, 500, 6200, 82251, 1142295, 16398200, 241379325, 3623534200, 55262073757, 853814730600, 13335836817420, 210225027967325, 3340362288091500, 53443628421286320, 860246972339613855, 13921016318025200505, 226352372251889455000, 3696160728052814340000
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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 = 5.
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LINKS
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FORMULA
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G.f. satisfies: A(x) = {1 + x*A(x)^(p/r)}^r, where p = 7, r = 5.
O.g.f. A(x) = 1/x * series reversion (x/C(x)^5), where C(x) is the o.g.f. for the Catalan numbers A000108. A(x)^(1/5) is the o.g.f. for A002296. - Peter Bala, Oct 14 2015
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MATHEMATICA
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Table[5 Binomial[7 n + 5, n]/(7 n + 5), {n, 0, 30}]
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PROG
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(PARI) a(n) = 5*binomial(7*n+5, n)/(7*n+5);
(PARI) {a(n)=local(B=1); for(i=0, n, B=(1+x*B^(7/5))^5+x*O(x^n)); polcoeff(B, n)}
(Magma) [5*Binomial(7*n+5, n)/(7*n+5): n in [0..30]];
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CROSSREFS
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Cf. A000108, A002296, A233832, A233833, A143547, A130565, A233835, A233907, A233908, A002296, A069271, A118970, A212073, A234465, A234510, A234571, A235339.
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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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