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 A213093 G.f. satisfies: A(x) = 1 + x/A(-x*A(x)^4). 23
 1, 1, 1, 4, 13, 62, 297, 1523, 8091, 43243, 234347, 1267141, 6814076, 36368431, 192079140, 1006805203, 5262612068, 27656507707, 147973596219, 815825605806, 4662818005761, 27504894986209, 165036600363916, 989160502170958, 5829789341752240, 33444482725193880 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Compare definition of g.f. to: (1) B(x) = 1 + x/B(-x*B(x)) when B(x) = 1/(1-x). (2) C(x) = 1 + x/C(-x*C(x)^3)^2 when C(x) = 1 + x*C(x)^2 is the g.f. of the Catalan numbers (A000108). (3) D(x) = 1 + x/D(-x*D(x)^5)^3 when D(x) = 1 + x*D(x)^3 is the g.f. of the ternary tree numbers (A001764). The first negative term is a(42) = -16825305705383790675462237694. - Georg Fischer, Feb 16 2019 LINKS Paul D. Hanna, Table of n, a(n) for n = 0..300 EXAMPLE G.f.: A(x) = 1 + x + x^2 + 4*x^3 + 13*x^4 + 62*x^5 + 297*x^6 + 1523*x^7 +... Related expansions: A(x)^4 = 1 + 4*x + 10*x^2 + 32*x^3 + 119*x^4 + 516*x^5 + 2462*x^6 +... A(-x*A(x)^4) = 1 - x - 3*x^2 - 6*x^3 - 31*x^4 - 141*x^5 - 697*x^6 - 3641*x^7 -... PROG (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1+x/subst(A, x, -x*subst(A^4, x, x+x*O(x^n))) ); polcoeff(A, n)} for(n=0, 30, print1(a(n), ", ")) CROSSREFS Cf. A000108, A001764, A213091, A213092, A213094, A213095, A213096. Sequence in context: A320359 A057712 A208592 * A135312 A287145 A266096 Adjacent sequences:  A213090 A213091 A213092 * A213094 A213095 A213096 KEYWORD sign AUTHOR Paul D. Hanna, Jun 05 2012 STATUS approved

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Last modified July 23 16:14 EDT 2019. Contains 325258 sequences. (Running on oeis4.)