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%I A213111 #5 Jun 06 2012 01:04:21
%S A213111 1,1,5,73,1497,48321,2016733,106687113,6745180529,495988880833,
%T A213111 41495596689141,3880618840698249,400537444634948041,
%U A213111 45126092520882513921,5501154522933362385485,720279890636684703825481,100658531630809161730405857,14934726665907895887483076737
%N A213111 E.g.f.: A(x) = exp( x/A(-x*A(x)^6)^2 ).
%C A213111 Compare the e.g.f. to:
%C A213111 (1) W(x) = exp(x/W(-x*W(x)^2)^1) when W(x) = Sum_{n>=0} (1*n+1)^(n-1)*x^n/n!.
%C A213111 (2) W(x) = exp(x/W(-x*W(x)^4)^2) when W(x) = Sum_{n>=0} (2*n+1)^(n-1)*x^n/n!.
%C A213111 (3) W(x) = exp(x/W(-x*W(x)^6)^3) when W(x) = Sum_{n>=0} (3*n+1)^(n-1)*x^n/n!.
%e A213111 E.g.f.: A(x) = 1 + x + 5*x^2/2! + 73*x^3/3! + 1497*x^4/4! + 48321*x^5/5! +...
%e A213111 Related expansions:
%e A213111 A(x)^2 = 1 + 2*x + 12*x^2/2! + 176*x^3/3! + 3728*x^4/4! + 118912*x^5/5! +...
%e A213111 A(x)^6 = 1 + 6*x + 60*x^2/2! + 1008*x^3/3! + 23952*x^4/4! + 775296*x^5/5! +...
%e A213111 1/A(-x*A(x)^6)^2 = 1 + 2*x + 20*x^2/2! + 296*x^3/3! + 7824*x^4/4! +...
%e A213111 The logarithm of the e.g.f., log(A(x)) = x/A(-x*A(x)^6)^2, begins:
%e A213111 log(A(x)) = x + 4*x^2/2! + 60*x^3/3! + 1184*x^4/4! + 39120*x^5/5! + 1639872*x^6/6! +...
%o A213111 (PARI) {a(n)=local(A=1+x);for(i=1,n,A=exp(x/subst(A^2,x,-x*A^6+x*O(x^n))));n!*polcoeff(A,n)}
%o A213111 for(n=0,25,print1(a(n),", "))
%Y A213111 Cf. A213108, A213109, A213110, A213112, A213113.
%K A213111 nonn
%O A213111 0,3
%A A213111 _Paul D. Hanna_, Jun 05 2012

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