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%I #3 Mar 30 2012 18:36:32
%S 1,1,3,6,16,38,103,268,738,2029,5723,16242,46762,135584,396702,
%T 1167986,3460931,10308313,30853232,92734392,279811894,847218649,
%U 2573387068,7839150746,23943472360,73310409148,224970044407,691817432334
%N Generating function satisfies A(x) = exp(A(x)x + 3A(x^2)x^2/2 + A(x^3)x^3/3 + 3A(x^4)x^4/4 +...).
%F A(x) = exp(sum_{n=1..inf} [2+(-1)^n]A(x^n)x^n/n), A(0)=1, where A(x)=1 + x + 3x^2 + 16x^3 + 38x^4 +103x^5 +...
%K easy,nonn
%O 0,3
%A _Paul D. Hanna_, Aug 17 2002
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