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 A179422 E.g.f.: A(x) = G(G(x)) = x*G'(x) where G(x) is the g.f. of A179420. 3

%I #4 Dec 31 2012 17:14:01

%S 1,4,36,528,11000,301680,10379376,433371008,21434318496,1232928216000,

%T 81297809313600,6074187611551488,509351655073262976,

%U 47554889211476564736,4909859201019880800000,557309205260654645145600

%N E.g.f.: A(x) = G(G(x)) = x*G'(x) where G(x) is the g.f. of A179420.

%H Paul D. Hanna, <a href="/A179422/b179422.txt">Table of n, a(n) for n = 1..150</a>

%F a(n) = n*A179420(n) = n^2*A179421(n-1).

%F E.g.f. satisfies: x*A'(x)/A(x) = G(A(x))/G(x) where G(x) is the g.f. of A179420.

%e E.g.f.: A(x) = x + 4*x^2/2! + 36*x^3/3! + 528*x^4/4! + 11000*x^5/5! +...

%e Let G(x) be the g.f. of A179420, then

%e . G(x) = x + 2*x^2/2! + 12*x^3/3! + 132*x^4/4! + 2200*x^5/5! +...

%e . G(G(x)) = x + 4*x^2/2! + 36*x^3/3! + 528*x^4/4! + 11000*x^5/5! + ...

%o (PARI) {a(n)=local(A=x+x^2+sum(m=3,n-1,a(m)*x^m/(m*m!))+x*O(x^n));if(n<3,n!*polcoeff(A,n),n*n!*polcoeff(subst(A,x,A),n)/(n-2))}

%Y Cf. A179420, A179421.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Jul 28 2010

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