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 A153291 G.f.: A(x) = F(x*F(x)) where F(x) = 1 + x*F(x)^3 is the g.f. of A001764. 1
 1, 1, 4, 21, 124, 782, 5145, 34873, 241682, 1704240, 12186900, 88162753, 644058237, 4744733614, 35210349041, 262976828766, 1975324849238, 14913200362138, 113107780322778, 861417424802187, 6585224638006020, 50515048389265713 (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-2k,n-k)*k/(3n-2k) for n>0 with a(0)=1. G.f. satisfies: A(x) = 1 + x*F(x)*A(x)^3 where F(x) is the g.f. of A001764. G.f. satisfies: A(x/G(x)) = F(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)) = 1 + x + 4*x^2 + 21*x^3 + 124*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)+k, n-k)*k/(3*(n-k)+k)))} CROSSREFS Cf. A001764; A153292. Sequence in context: A108404 A115136 A101478 * A244062 A093965 A195262 Adjacent sequences:  A153288 A153289 A153290 * A153292 A153293 A153294 KEYWORD nonn AUTHOR Paul D. Hanna, Jan 14 2009 STATUS approved

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Last modified June 22 20:16 EDT 2021. Contains 345388 sequences. (Running on oeis4.)