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A161797
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G.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^3).
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2
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1, 1, 4, 16, 71, 336, 1660, 8464, 44207, 235306, 1271807, 6961307, 38508659, 214950425, 1209170536, 6848080767, 39014400171, 223439516338, 1285660965508, 7428738358924, 43087099589998, 250766507928988, 1464026402082801
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OFFSET
| 0,3
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FORMULA
| a(n) = Sum_{k=0..n} C(n,k)/(n-k+1) * C(n+2*k-1,n-k).
Let A(x)^m = Sum_{n>=0} a(n,m)*x^n then
a(n,m) = Sum_{k=0..n} C(n+m-1,k)*m/(n-k+m) * C(n+2*k-1,n-k).
G.f.: A(x) = (1/x)*serreverse[x/(1 + x/(1 - x)^3)].
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PROG
| (PARI) {a(n, m=1)=sum(k=0, n, binomial(n+m-1, k)*m/(n-k+m)*binomial(n+2*k-1, n-k))}
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CROSSREFS
| Cf. A109081.
Sequence in context: A133789 A151244 A091354 * A124533 A158784 A180141
Adjacent sequences: A161794 A161795 A161796 * A161798 A161799 A161800
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jun 19 2009
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