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%I #5 Mar 30 2012 18:37:33
%S 1,4,54,1528,74200,5513088,581644210,82684556736,15235237204524,
%T 3531551323602720,1005740523344585424,345183221074356437760,
%U 140516542507328903804616,66939548487495601942276224,36891997133237736166187224200
%N a(n) = [x^n/n!] 1 - (1-x)^(1/(1 + n*log(1-x))).
%F a(n) equals the coefficient of x^n/n! in the n-th iteration of 1 - (1-x)^(1/(1 + log(1-x))).
%e Let G(x) = 1 - (1-x)^(1/(1 + log(1-x))); the iterations of G(x) begin:
%e G(x) = x + 2*x^2/2! + 6*x^3/3! + 22*x^4/4! + 80*x^5/5! + 98*x^6/6! +...
%e G(G(x)) = x + 4*x^2/2! + 24*x^3/3! + 188*x^4/4! + 1780*x^5/5! +...
%e G(G(G(x))) = x + 6*x^2/2! + 54*x^3/3! + 642*x^4/4! + 9420*x^5/5! +...
%e G(G(G(G(x)))) = x + 8*x^2/2! + 96*x^3/3! + 1528*x^4/4! + 30200*x^5/5! +...
%e G(G(G(G(G(x))))) = x + 10*x^2/2! + 150*x^3/3! + 2990*x^4/4! + 74200*x^5/5! +...
%o (PARI) {a(n)=n!*polcoeff(1-(1-x+x*O(x^n))^(1/(1+n*log(1-x+x*O(x^n)))),n)}
%Y Cf. A203038.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Dec 27 2011
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