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 A186632 E.g.f. satisfies: A(A(A(x))) = d/dx A(x)^2/2 with A(0)=0, A'(0)=1. 0
 1, 2, 24, 588, 22560, 1201320, 82875744, 7085373456, 727827579648, 87810122446560, 12227912455651200, 1938610503725962176, 346053263639068417536, 68919212804888587849344 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS FORMULA E.g.f. satisfies: A(A(A(x))) = A'(x)*A(x). E.g.f. satisfies: A(A(A(A(x)))) = A'(A(x))*A(A(x)) = A( A'(x)*A(x) ). E.g.f. satisfies: A(A(A(A(A(x))))) = A'(A(A(x)))*A'(x)*A(x). n(n-1) divides a(n) for n>=2. EXAMPLE E.g.f: A(x) = x + 2*x^2/2! + 24*x^3/3! + 588*x^4/4! + 22560*x^5/5! +... A(x)^2/2 = x^2/2! + 6*x^3/3! + 108*x^4/4! + 3420*x^5/5! + 158760*x^6/6! +... Iterations of the e.g.f. begin: A(A(x)) = x + 4*x^2/2! + 60*x^3/3! + 1680*x^4/4! + 70920*x^5/5! +... A(A(A(x))) = x + 6*x^2/2! + 108*x^3/3! + 3420*x^4/4! + 158760*x^5/5! +... A(A(A(A(x)))) = x + 8*x^2/2! + 168*x^3/3! + 5952*x^4/4! + 302640*x^5/5! +... A(A(A(A(A(x))))) = x + 10*x^2/2! + 240*x^3/3! + 9420*x^4/4! + 522000*x^5/5! +... Related expansions: A'(A(x)) = 1 + 2*x + 28*x^2/2! + 780*x^3/3! + 33384*x^4/4! + 1956120*x^5/5! +... A'(A(A(x))) = 1 + 2*x + 32*x^2/2! + 996*x^3/3! + 46944*x^4/4! + 2998680*x^5/5! +... PROG (PARI) {a(n)=local(A=x+x^2+sum(m=3, n-1, a(m)*x^m/m!)+x*O(x^n)); if(n<3, n!*polcoeff(A, n), n!*polcoeff(subst(A, x, subst(A, x, A))-deriv(A^2/2), n)/(n-2))} CROSSREFS Cf. A179420. Sequence in context: A280794 A090316 A128578 * A089835 A210909 A009251 Adjacent sequences:  A186629 A186630 A186631 * A186633 A186634 A186635 KEYWORD nonn AUTHOR Paul D. Hanna, Feb 24 2011 STATUS approved

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Last modified December 8 09:32 EST 2019. Contains 329862 sequences. (Running on oeis4.)