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 A193264 E.g.f. A(x) satisfies: A(A(A(x))) = 2*x*A'(x) - A(x), where A(x) = Sum_{n>=1} a(n)*x^n, with a(1)=1, a(2)=2. 2
 1, 2, 18, 324, 9140, 359460, 18408600, 1174201280, 90423766800, 8215991163000, 865420074120800, 104218992780067440, 14188585798246317120, 2163608674997595229040, 366682177870608886473600, 68611838511981521881152000, 14093827998013078645611495680 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Paul D. Hanna, Table of n, a(n) for n = 1..150 FORMULA E.g.f. A(x) satisfies: A(A(A(x))) = Sum_{n>=1} (2*n-1)*a(n)*x^n. a(n) = n*A193265(n-1). EXAMPLE E.g.f.: A(x) = x + 2*x^2/2! + 18*x^3/3! + 324*x^4/4! + 9140*x^5/5! + 359460*x^6/6! +...+ a(n)*x^n/n! +... where A(A(A(x))) = x + 6*x^2/2! + 90*x^3/3! + 2268*x^4/4! + 82260*x^5/5! + 3954060*x^6/6! +...+ (2*n-1)*a(n)*x^n/n! +... which equals: 2*x*A'(x) - A(x) = x + 3*2*x^2/2! + 5*18*x^3/3! + 7*324*x^4/4! + 9*9140*x^5/5! +... PROG (PARI) {a(n)=local(A=x); if(n<1, 0, if(n<=2, n, A=x+sum(m=2, n-1, a(m)*x^m/m!)+x*O(x^n); n!*polcoeff(subst(A, x, subst(A, x, A))-2*x*A', n)/(2*n-4)))} CROSSREFS Cf. A193265, A179420. Sequence in context: A087215 A229490 A192985 * A191492 A090307 A123311 Adjacent sequences:  A193261 A193262 A193263 * A193265 A193266 A193267 KEYWORD nonn AUTHOR Paul D. Hanna, Jul 20 2011 STATUS approved

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