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A172394 G.f. satisfies: A(x) = G(x/A(x)) where o.g.f. G(x) = A(x*G(x)) = Sum_{n>=0} A001464(n)*x^n.

%I A172394 #2 Mar 30 2012 18:37:21
%S A172394 1,-1,-1,0,1,0,-4,0,27,0,-248,0,2830,0,-38232,0,593859,0,-10401712,0,
%T A172394 202601898,0,-4342263000,0,101551822350,0,-2573779506192,0,
%U A172394 70282204726396,0,-2057490936366320,0,64291032462761955,0
%N A172394 G.f. satisfies: A(x) = G(x/A(x)) where o.g.f. G(x) = A(x*G(x)) = Sum_{n>=0} A001464(n)*x^n.
%C A172394 The e.g.f. of A001464 is exp(-x-x^2/2) = Sum_{n>=0} A001464(n)*x^n/n!.
%F A172394 a(2n-2) = (-1)^(n-1)*A000699(n), where A000699(n) is the number of irreducible diagrams with 2n nodes, for n>=1.
%F A172394 a(2n-1) = 0 for n>=2, with a(1) = -1.
%e A172394 G.f.: A(x) = 1 - x - x^2 + x^4 - 4*x^6 + 27*x^8 - 248*x^10 +...
%e A172394 where G(x) = A(x*G(x)) is the o.g.f. of A001464:
%e A172394 G(x) = 1 - x + 2*x^3 - 2*x^4 - 6*x^5 + 16*x^6 + 20*x^7 - 132*x^8 +...
%e A172394 while the e.g.f. of A001464 is given by:
%e A172394 exp(-x-x^2/2) = 1 - x + 2*x^3/3! - 2*x^4/4! - 6*x^5/5! + 16*x^6/6! +...
%o A172394 (PARI) {a(n)=local(G=sum(m=0,n,m!*polcoeff(exp(-x-x^2/2+x*O(x^m)),m)*x^m)+x*O(x^n));polcoeff(x/serreverse(x*G),n)}
%Y A172394 Cf. A001464, A000699, A172395 (variant).
%K A172394 sign
%O A172394 0,7
%A A172394 _Paul D. Hanna_, Feb 06 2010