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 A193099 E.g.f. A(x) satisfies: A'(x) = 1 + A(A(A(A(x)))). 1
 1, 1, 4, 34, 466, 9044, 230827, 7388781, 287044354, 13212057907, 707417718215, 43431362340153, 3022050938855344, 236053437141340206, 20532456001485751429, 1975258248906891145913, 208928124926501980596761, 24172548454436633069025270 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS EXAMPLE E.g.f.: A(x) = x + x^2/2! + 4*x^3/3! + 34*x^4/4! + 466*x^5/5! + 9044*x^6/6! +... where the derivative of the e.g.f. begins: A'(x) = 1 + x + 4*x^2/2! + 34*x^3/3! + 466*x^4/4! + 9044*x^5/5! +... Related expansions. A(A(x)) = x + 2*x^2/2! + 11*x^3/3! + 111*x^4/4! + 1702*x^5/5! + 35854*x^6/6! +... A(A(A(x))) = x + 3*x^2/2! + 21*x^3/3! + 249*x^4/4! + 4303*x^5/5! + 99650*x^6/6! +... A(A(A(A(x)))) = x + 4*x^2/2! + 34*x^3/3! + 466*x^4/4! + 9044*x^5/5! +... PROG (PARI) {a(n)=local(A=x); for(i=1, n, A=intformal(1+subst(A, x, subst(A, x, subst(A, x, A+O(x^(n+1))))))); n!*polcoeff(A, n)} CROSSREFS Cf. A001028, A193098, A193100, A179420. Sequence in context: A218674 A321264 A234291 * A208831 A294475 A198976 Adjacent sequences:  A193096 A193097 A193098 * A193100 A193101 A193102 KEYWORD nonn AUTHOR Paul D. Hanna, Jul 15 2011 STATUS approved

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Last modified June 19 19:11 EDT 2019. Contains 324222 sequences. (Running on oeis4.)