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 A193098 E.g.f. A(x) satisfies: A'(x) = 1 + A(A(A(x))). 1
 1, 1, 3, 18, 171, 2283, 39942, 874944, 23243829, 731486637, 26782956144, 1124838704976, 53567894139165, 2865318598843281, 170774893724336223, 11264050942430761881, 817374450539598433587, 64917115563124199691834 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Table of n, a(n) for n=1..18. EXAMPLE E.g.f.: A(x) = x + x^2/2! + 3*x^3/3! + 18*x^4/4! + 171*x^5/5! + 2283*x^6/6! +... where the derivative of the e.g.f. begins: A'(x) = 1 + x + 3*x^2/2! + 18*x^3/3! + 171*x^4/4! + 2283*x^5/5! +... Related expansions. A(A(x)) = x + 2*x^2/2! + 9*x^3/3! + 69*x^4/4! + 777*x^5/5! + 11802*x^6/6! + 229047*x^7/7! + 5472600*x^8/8! +... A(A(A(x))) = x + 3*x^2/2! + 18*x^3/3! + 171*x^4/4! + 2283*x^5/5! +... PROG (PARI) {a(n)=local(A=x); for(i=1, n, A=intformal(1+subst(A, x, subst(A, x, A+O(x^(n+1)))))); n!*polcoeff(A, n)} CROSSREFS Cf. A001028, A193099, A193100, A179420. Sequence in context: A113130 A367373 A289683 * A322771 A177447 A328031 Adjacent sequences: A193095 A193096 A193097 * A193099 A193100 A193101 KEYWORD nonn AUTHOR Paul D. Hanna, Jul 15 2011 STATUS approved

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Last modified August 8 08:46 EDT 2024. Contains 375018 sequences. (Running on oeis4.)