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A161799
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G.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^2)^3.
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1
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1, 3, 12, 61, 345, 2085, 13182, 86106, 576543, 3936029, 27294390, 191722887, 1361291244, 9754412169, 70447946556, 512278417176, 3747570671685, 27561220671408, 203657352324178, 1511270129552163, 11257532921742528
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OFFSET
| 0,2
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FORMULA
| a(n) = Sum_{k=0..n} C(3*n-2*k+2,k)/(n-k+1) * C(n+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(3*n-2*k+3*m-1,k)*m/(n-k+m) * C(n+k-1,n-k).
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PROG
| (PARI) {a(n, m=1)=sum(k=0, n, binomial(3*n-2*k+3*m-1, k)*m/(n-k+m)*binomial(n+k-1, n-k))}
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CROSSREFS
| Cf. A161797, A161798.
Sequence in context: A078162 A002497 A192479 * A182970 A159925 A121694
Adjacent sequences: A161796 A161797 A161798 * A161800 A161801 A161802
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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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