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 A120900 G.f. satisfies: A(x) = C(x)*A(x^3*C(x)^4), where C(x) is the g.f. of the Catalan numbers (A000108). 3
 1, 1, 2, 6, 19, 62, 209, 722, 2539, 9054, 32654, 118876, 436171, 1611067, 5984943, 22344455, 83786875, 315397144, 1191324649, 4513742858, 17149228138, 65318912291, 249356597492, 953902701488, 3656057618727, 14037222220896 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Self-convolution equals A120899, which equals column 0 of triangle A120898 (cascadence of 1+2x+x^2). LINKS EXAMPLE A(x) = 1 + x + 2*x^2 + 6*x^3 + 19*x^4 + 62*x^5 + 209*x^6 + 722*x^7 +... = C(x) * A(x^3*C(x)^4) where C(x) = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 42*x^5 + 132*x^6 +... is the g.f. of the Catalan numbers (A000108): C(x) = 1 + x*C(x)^2. PROG (PARI) {a(n)=local(A=1+x, C=(1/x*serreverse(x/(1+2*x+x^2+x*O(x^n))))^(1/2)); for(i=0, n, A=C*subst(A, x, x^3*C^4 +x*O(x^n))); polcoeff(A, n, x)} CROSSREFS Cf. A120898, A120899, A000108. Sequence in context: A071738 A026012 A191993 * A284216 A059712 A059713 Adjacent sequences:  A120897 A120898 A120899 * A120901 A120902 A120903 KEYWORD nonn AUTHOR Paul D. Hanna, Jul 14 2006 STATUS approved

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Last modified September 21 04:10 EDT 2021. Contains 347596 sequences. (Running on oeis4.)