A193098 E.g.f. A(x) satisfies: A'(x) = 1 + A(A(A(x))).

1, 1, 3, 18, 171, 2283, 39942, 874944, 23243829, 731486637, 26782956144, 1124838704976, 53567894139165, 2865318598843281, 170774893724336223, 11264050942430761881, 817374450539598433587, 64917115563124199691834

Offset: 1

Author

Paul D. Hanna, Jul 15 2011

Keywords

• nonn

Examples

			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! +...
		

Crossrefs

Cf. A001028, A193099, A193100, A179420.

Programs

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)}