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 A143135 E.g.f. satisfies: A(x) = sin(x + A(x)^2) with A(0)=0. 2
 1, 2, 11, 100, 1261, 20342, 399671, 9256840, 246907321, 7452534122, 251099460611, 9341422237420, 380293239870181, 16815919738248542, 802553031266952431, 41117164304824602640, 2250747364089063475441 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Radius of convergence of A(x) is r = Pi/4 - 1/2, with A(r) = sqrt(2)/2. LINKS FORMULA E.g.f.: A(x) = sin(G(x)) where G(x) = x + A(x)^2 is the e.g.f. of A143134. E.g.f. derivative: A'(x) = sqrt(1 - A(x)^2)/(1 - 2*A(x)*sqrt(1 - A(x)^2)). EXAMPLE A(x) = x + 2*x^2/2! + 11*x^3/3! + 100*x^4/4! + 1261*x^5/5! +... A(x) = sin(G(x)) where G(x) = x + A(x)^2 is the e.g.f. of A143134: G(x) = x + 2*x^2/2! + 12*x^3/3! + 112*x^4/4! + 1440*x^5/5! +... PROG (PARI) {a(n)=local(A=x); for(i=0, n, A=x + sin(A)^2); n!*polcoeff(sin(A), n)} (PARI) {a(n)=n!*polcoeff(sin(serreverse(x-sin(x+x*O(x^n))^2)), n)} CROSSREFS Cf. A143134, A143137. Sequence in context: A020559 A003579 A099169 * A205806 A220433 A056732 Adjacent sequences:  A143132 A143133 A143134 * A143136 A143137 A143138 KEYWORD nonn AUTHOR Paul D. Hanna, Jul 27 2008 STATUS approved

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