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 A153292 G.f.: A(x) = F(x*F(x)^2) where F(x) = 1 + x*F(x)^3 is the g.f. of A001764. 2
 1, 1, 5, 31, 211, 1516, 11295, 86423, 675051, 5361323, 43171480, 351709926, 2894115003, 24022408477, 200918146461, 1691749323232, 14329850844625, 122028162988698, 1044131083377287, 8972696721635997, 77408293908402336 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA a(n) = Sum_{k=0..n} C(3k+1,k)/(3k+1) * C(3n-k,n-k)*2k/(3n-k) for n>0 with a(0)=1. G.f. satisfies: A(x) = 1 + x*F(x)^2*A(x)^3 where F(x) is the g.f. of A001764. G.f. satisfies: A(x/G(x)) = F(x*G(x)) where G(x) = F(x/G(x)) is the g.f. of A000108 and F(x) is the g.f. of A001764. EXAMPLE G.f.: A(x) = F(x*F(x)^2) = 1 + x + 5*x^2 + 31*x^3 + 211*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 +... PROG (PARI) {a(n)=if(n==0, 1, sum(k=0, n, binomial(3*k+1, k)/(3*k+1)*binomial(3*(n-k)+2*k, n-k)*2*k/(3*(n-k)+2*k)))} CROSSREFS Cf. A001764, A000108; A153293. Sequence in context: A247639 A002649 A104091 * A087457 A146962 A269730 Adjacent sequences:  A153289 A153290 A153291 * A153293 A153294 A153295 KEYWORD nonn AUTHOR Paul D. Hanna, Jan 14 2009 STATUS approved

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Last modified October 15 03:16 EDT 2019. Contains 328025 sequences. (Running on oeis4.)