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Search: id:A153293
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| A153293 |
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G.f.: A(x) = F(x*F(x)^3) = F(F(x)-1) where F(x) = 1 + x*F(x)^3 is the g.f. of A001764. |
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+0
3
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| 1, 1, 6, 42, 317, 2508, 20517, 172180, 1474689, 12843768, 113444721, 1014062898, 9158151426, 83449247979, 766340138037, 7085966319858, 65919413472834, 616559331247512, 5794778945023698, 54700034442193302, 518375457403431600
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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a(n) = Sum_{k=0..n} C(3k+1,k)/(3k+1) * C(3n,n-k)*k/n for n>0 with a(0)=1.
G.f. satisfies: A(x) = 1 + x*F(x)^3*A(x)^3 where F(x) is the g.f. of A001764.
G.f. satisfies: A(x/G(x)) = F(x*G(x)^2) = F(G(x)-1) where G(x) = F(x/G(x)) is the g.f. of A000108 and F(x) is the g.f. of A001764.
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EXAMPLE
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G.f.: A(x) = F(x*F(x)^3) = 1 + x + 6*x^2 + 42*x^3 + 317*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 +...
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PROGRAM
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(PARI) {a(n)=if(n==0, 1, sum(k=0, n, binomial(3*k+1, k)/(3*k+1)*binomial(3*(n-k)+3*k, n-k)*3*k/(3*(n-k)+3*k)))}
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CROSSREFS
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Cf. A001764, A000108; A153292, A153294.
Sequence in context: A093388 A162968 A034171 this_sequence A145301 A107266 A142985
Adjacent sequences: A153290 A153291 A153292 this_sequence A153294 A153295 A153296
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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 14 2009
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