A193099 - OEIS

%I #6 Mar 30 2012 18:37:27

%S 1,1,4,34,466,9044,230827,7388781,287044354,13212057907,707417718215,

%T 43431362340153,3022050938855344,236053437141340206,

%U 20532456001485751429,1975258248906891145913,208928124926501980596761,24172548454436633069025270

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

%e  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! +...

%e where the derivative of the e.g.f. begins:

%e A'(x) = 1 + x + 4*x^2/2! + 34*x^3/3! + 466*x^4/4! + 9044*x^5/5! +...

%e Related expansions.

%e A(A(x)) = x + 2*x^2/2! + 11*x^3/3! + 111*x^4/4! + 1702*x^5/5! + 35854*x^6/6! +...

%e 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! +...

%e A(A(A(A(x)))) = x + 4*x^2/2! + 34*x^3/3! + 466*x^4/4! + 9044*x^5/5! +...

%o  (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)}

%Y  Cf. A001028, A193098, A193100, A179420.

%K nonn

%O 1,3

%A _Paul D. Hanna_, Jul 15 2011