A193100 - OEIS

%I #9 Mar 30 2012 18:37:27

%S 1,3,63,6804,1990170,1145276496,1172421884088,1981846981092069,

%T 5166650461467914874,19710026486212156729362,

%U 105613632141369240315500892,768455476842781911036557334267,7380326961188107570497477933701847

%N E.g.f. A(x) satisfies:  A’(x) = x + A(A(x)), where A(x) = Sum_{n>=0} a(n)*x^(3*n+2)/(3*n+2)!.

%e E.g.f.: A(x) = x^2/2! + 3*x^5/5! + 63*x^8/8! + 6804*x^11/11! + 1990170*x^14/14! + 1145276496*x^17/17! + 1172421884088*x^20/20! +...

%e where A'(x) = x + 3*x^4/4! + 63*x^7/7! + 6804*x^10/10! +...

%e and A(A(x)) = 3*x^4/4! + 63*x^7/7! + 6804*x^10/10! + 1990170*x^13/13! +...

%o (PARI) {a(n)=local(A=x^2/2);for(i=1,n,A=intformal(x+subst(A,x,A+O(x^(3*n+3)))));(3*n+2)!*polcoeff(A,3*n+2)}

%Y Cf. A001028, A179420.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jul 15 2011