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 A185754 G.f. satisfies: A(x) = x + x*sqrt(A(A(x)) - A(x)). 1
 1, 1, 2, 7, 36, 243, 2016, 19745, 222318, 2824546, 39938124, 621808679, 10569132576, 194745803641, 3866820606006, 82313887902511, 1870203518285750, 45174881008705328, 1156071783429567906, 31246398342838909318 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS FORMULA Let F(x) be the g.f. of A185753, then g.f. A(x) satisfies: * A(x) = x + (F(x)-1)^2, * A(x) = x*F(A(x)), * A(x) = Series_Reversion(x/F(x)). EXAMPLE G.f.: A(x) = x + x^2 + 2*x^3 + 7*x^4 + 36*x^5 + 243*x^6 +... A(A(x)) = x + 2*x^2 + 6*x^3 + 25*x^4 + 136*x^5 + 922*x^6 + 7524*x^7 +... The g.f. of A185753 begins: F(x) = 1 + x + x^2 + 3*x^3 + 15*x^4 + 102*x^5 + 861*x^6 + 8593*x^7 +... where (F(x)-1)^2 = x^2 + 2*x^3 + 7*x^4 + 36*x^5 + 243*x^6 + 2016*x^7 +... F(A(x)) = 1 + x + 2*x^2 + 7*x^3 + 36*x^4 + 243*x^5 + 2016*x^6 +... PROG (PARI) {a(n)=local(A=x+x^2); for(i=1, n, A=2*A-x-(x/serreverse(A+x*O(x^n))-1)^2); polcoeff(A, n)} CROSSREFS Cf. A185753. Sequence in context: A088715 A088313 A201197 * A191493 A095793 A029768 Adjacent sequences:  A185751 A185752 A185753 * A185755 A185756 A185757 KEYWORD nonn AUTHOR Paul D. Hanna, Feb 02 2011 STATUS approved

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Last modified May 16 08:07 EDT 2021. Contains 343940 sequences. (Running on oeis4.)