A202669 - OEIS

%I #21 Mar 30 2012 18:37:33

%S 1,0,2,2,12,20,96,212,898,2354,9266,27070,102094,319930,1177838,

%T 3865762,14050948,47574460,171886784,594572676,2143957648,7528825924,

%U 27156892364,96412294088,348314869652,1246689890248,4513958859208,16257651642036,59010423148052,213586733348928

%N G.f. satisfies: A(x) = exp( Sum_{n>=1} (A(x) + (-1)^n)^n * x^n/n ).

%F G.f. satisfies: A(x) = 1/(1-x*A(x)) * exp( Sum_{n>=1} (-1)^n/(1 - (-1)^n*x*A(x))^n * x^n/n ).

%F G.f. satisfies: A(x) = sqrt( (1 - (A(x)-1)^2*x^2)/(1 - (A(x)+1)^2*x^2) ) / (1 - (A(x)-1)*x).

%F G.f. satisfies: 0 = -(1-x) - x*A(x) + (1-x)*(1+x)^2*A(x)^2 - x*(1+x)^2*A(x)^3 - x^2*(1-x)*A(x)^4 + x^3*A(x)^5.

%e G.f.: A(x) = 1 + 2*x^2 + 2*x^3 + 12*x^4 + 20*x^5 + 96*x^6 + 212*x^7 +...

%e where

%e log(A(x)) = (A(x) - 1)*x + (A(x) + 1)^2*x^2/2 + (A(x) - 1)^3*x^3/3 + (A(x) + 1)^4*x^4/4 +...

%e log(A(x)*(1-x*A(x))) = -1/(1 + x*A(x))*x + 1/(1 - x*A(x))^2*x^2/2 - 1/(1 + x*A(x))^3*x^3/3 + 1/(1 - x*A(x))^4*x^4/4 +...

%o (PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, (A+(-1)^m+x*O(x^n))^m*x^m/m))); polcoeff(A, n)}

%Y Cf. A202668, A202629, A202519, A155200.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Dec 22 2011