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 A112806 Expansion of solution of functional equation. 1
 1, 1, 2, 6, 21, 79, 312, 1277, 5369, 23049, 100612, 445214, 1992606, 9004260, 41025315, 188259072, 869305315, 4036286518, 18832973733, 88259024068, 415252542641, 1960718710035, 9288106921038, 44129146527731 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA Given g.f. A(x), then series reversion of B(x)=x*A(x^3) is -B(-x). Given g.f. A(x), then y=x*A(x^3) satisfies y=x+(xy)^2/(1-(xy)^3). G.f. satisfies: A(x) = 1 + x*A(x)^2/(1 - x^2*A(x)^3). - Paul D. Hanna, Jun 06 2012 G.f. satisfies: A(x) = 1/A(-x*A(x)^3); note that the Catalan function C(x) = 1 + x*C(x)^2 (A000108) also satisfies this condition. - Paul D. Hanna, Jun 06 2012 PROG (PARI) {a(n)=local(A); if(n<0, 0, A=x+O(x^4); for(k=1, n, A=x+subst(x^2/(1-x^3), x, x*A)); polcoeff(A, 3*n+1))} (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1+x*A^2/(1-x^2*A^3)); polcoeff(A, n)} \\ Paul D. Hanna, Jun 06 2012 CROSSREFS Cf. A216490. Sequence in context: A150198 A033321 A050203 * A150199 A150200 A150201 Adjacent sequences:  A112803 A112804 A112805 * A112807 A112808 A112809 KEYWORD nonn AUTHOR Michael Somos, Sep 20 2005 STATUS approved

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