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A196562 E.g.f. satisfies: A(x) = 1 + Sum{n>=1} x^n * A(n^2*x)^(1/n) / n!.

%I A196562 #7 Mar 30 2012 18:37:31
%S A196562 1,1,3,16,197,5556,402727,68650114,28060721817,25837746071608,
%T A196562 54301560755743691,252957269930383300734,2621503487300921168212357,
%U A196562 59671929727060536957652131604,2977392188346587645059521680164959
%N A196562 E.g.f. satisfies: A(x) = 1 + Sum{n>=1} x^n * A(n^2*x)^(1/n) / n!.
%e A196562 E.g.f.: A(x) = 1 + x + 3*x^2/2! + 16*x^3/3! + 197*x^4/4! + 5556*x^5/5! +...
%e A196562 where
%e A196562 A(x) = 1 + x*A(x) + x^2*A(4*x)^(1/2)/2! + x^3*A(9*x)^(1/3)/3! + x^4*A(16*x)^(1/4)/4! +...
%e A196562 Related expansions begin:
%e A196562 A(4*x)^(1/2) = 1 + 2*x + 20*x^2/2! + 392*x^3/3! + 20880*x^4/4! +...
%e A196562 A(9*x)^(1/3) = 1 + 3*x + 63*x^2/2! + 2700*x^3/3! + 335421*x^4/4! +...
%e A196562 A(16*x)^(1/4) = 1 + 4*x + 144*x^2/2! + 10816*x^3/3! + 2437376*x^4/4! +...
%e A196562 A(25*x)^(1/5) = 1 + 5*x + 275*x^2/2! + 32000*x^3/3! + 11413125*x^4/4! +...
%e A196562 A(36*x)^(1/6) = 1 + 6*x + 468*x^2/2! + 77976*x^3/3! + 40405392*x^4/4! +...
%o A196562 (PARI) {a(n)=local(A=1+x);for(i=1,n,A=1+sum(m=1,n,x^m/m!*subst(A,x,m^2*x+x*O(x^n))^(1/m)));n!*polcoeff(A,n)}
%Y A196562 Cf. A196561, A125281.
%K A196562 nonn
%O A196562 0,3
%A A196562 _Paul D. Hanna_, Oct 03 2011