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A196022 E.g.f. satisfies: A(x) = Sum_{n>=0} 1/n! * Sum_{k=0..n} C(n,k)*(1 + x/2*A(x)^(n-k))^(n-k) * (-1 + x/2*A(x)^k)^k.

%I A196022 #15 Mar 30 2012 18:37:29
%S A196022 1,1,3,22,269,4676,106027,2966909,98814921,3818572219,167999566061,
%T A196022 8292669672343,453958089569833,27300462412168531,1789601591598075179,
%U A196022 127031469572649790786,9709396866317453042033,795229841271312470470904,69499103185446754949076817
%N A196022 E.g.f. satisfies: A(x) = Sum_{n>=0} 1/n! * Sum_{k=0..n} C(n,k)*(1 + x/2*A(x)^(n-k))^(n-k) * (-1 + x/2*A(x)^k)^k.
%e A196022 E.g.f.: A(x) = 1 + x + 3*x^2/2! + 22*x^3/3! + 269*x^4/4! + 4676*x^5/5! +...
%e A196022 where e.g.f. A = A(x) satisfies:
%e A196022 A(x) = 1 + ((1+x/2*A) + (-1+x/2*A)) +
%e A196022 1/2!*((1+x/2*A^2)^2 + 2*(1+x/2*A)*(-1+x/2*A) + (-1+x/2*A^2)^2) +
%e A196022 1/3!*((1+x/2*A^3)^3 + 3*(1+x/2*A^2)^2*(-1+x/2*A) + 3*(1+x/2*A)*(-1+x/2*A^2)^2 + (-1+x/2*A^3)^3) +
%e A196022 1/4!*((1+x/2*A^4)^4 + 4*(1+x/2*A^3)^3*(-1+x/2*A) + 6*(1+x/2*A^2)^2*(-1+x/2*A^2)^2 + 4*(1+x/2*A)*(-1+x/2*A^3)^3 + (-1+x/2*A^4)^4) +
%e A196022 1/5!*((1+x/2*A^5)^5 + 5*(1+x/2*A^4)^4*(-1+x/2*A) + 10*(1+x/2*A^3)^3*(-1+x/2*A^2)^2 + 10*(1+x/2*A^2)^2*(-1+x/2*A^3)^3 + 5*(1+x/2*A)*(-1+x/2*A^4)^4 + (-1+x/2*A^5)^5) +...
%o A196022 (PARI) {a(n)=local(A=1+x,X=x+x*O(x^n));for(i=1,n,A=1+sum(m=1,n,1/m!*sum(k=0,m,binomial(m,k)*(1+X/2*A^(m-k))^(m-k)*(-1+X/2*A^k)^k)));n!*polcoeff(A,n)}
%K A196022 nonn
%O A196022 0,3
%A A196022 _Paul D. Hanna_, Sep 26 2011