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Search: id:A153390
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| A153390 |
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G.f.: A(x) = F(x*G(x))^2 where F(x) = G(x*F(x)) = 1 + x*F(x)^3 is the g.f. of A001764 and G(x) = F(x/G(x)) = 1 + x*G(x)^2 is the g.f. of A000108 (Catalan). |
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+0
3
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| 1, 2, 9, 48, 278, 1696, 10736, 69886, 465019, 3149476, 21643433, 150554144, 1058101315, 7502183626, 53599160532, 385494328218, 2788827078507, 20280590381098, 148167425970522, 1087007419753186, 8004683588800899
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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a(n) = Sum_{k=0..n} C(3k+2,k)*2/(3k+2) * C(2n-k,n-k)*k/(2n-k) for n>0 with a(0)=1.
G.f. satisfies: A(x*F(x)) = F(x*F(x)^2)^2 where F(x) is the g.f. of A001764.
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EXAMPLE
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G.f.: A(x) = F(x*G(x))^2 = 1 + 2*x + 9*x^2 + 48*x^3 + 278*x^4 +... where
F(x) = 1 + x + 3*x^2 + 12*x^3 + 55*x^4 + 273*x^5 + 1428*x^6 +...
F(x)^2 = 1 + 2*x + 7*x^2 + 30*x^3 + 143*x^4 + 728*x^5 + 3876*x^6 +...
F(x)^3 = 1 + 3*x + 12*x^2 + 55*x^3 + 273*x^4 + 1428*x^5 + 7752*x^6 +...
G(x) = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 42*x^5 + 132*x^6 +...
G(x)^2 = 1 + 2*x + 5*x^2 + 14*x^3 + 42*x^4 + 132*x^5 + 429*x^6 +...
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PROGRAM
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(PARI) {a(n)=if(n==0, 1, sum(k=0, n, binomial(3*k+2, k)*2/(3*k+2)*binomial(2*(n-k)+k, n-k)*k/(2*(n-k)+k)))}
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CROSSREFS
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Cf. A000108, A001764; A153299, A153391.
Sequence in context: A047139 A047059 A153297 this_sequence A118341 A100427 A074143
Adjacent sequences: A153387 A153388 A153389 this_sequence A153391 A153392 A153393
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jan 15 2009
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