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%I #3 Mar 30 2012 18:37:15
%S 1,1,4,31,373,6250,136711,3740137,124143598,4887140221,224203589593,
%T 11819532185476,707883494843341,47708648339054629,3589347850731252292,
%U 299381557667730507907,27518788652896695773041
%N Row 2 of square table A145085.
%C Let S(n,x) be the e.g.f. of row n of square table A145085, then the e.g.f.s satisfy: S(n,x) = exp( Integral S(n+1,x)^(n+1) dx ) for n>=0.
%F E.g.f.: A(x) = S(2,x) = exp( Integral S(3,x)^3 dx ) where S(n,x) is the e.g.f. of row n of square table A145085.
%F E.g.f.: A(x) = R(2,x)^(1/2) = exp( Integral R(3,x) dx ) where R(2,x) = e.g.f. of A145082 and R(3,x) = e.g.f. of A145083.
%o (PARI) {a(n)=local(A=vector(n+3,j,1+j*x)); for(i=0,n+2,for(j=0,n,m=n+2-j;A[m]=exp(m*intformal(A[m+1]+x*O(x^n))))); n!*polcoeff(A[2]^(1/2),n,x)}
%o (PARI) {a(n)=local(A=vector(n+3,j,1+j*x)); for(i=0,n+2,for(j=0,n,m=n+2-j;A[m]=exp(intformal(A[m+1]^(m+1)+x*O(x^n))))); n!*polcoeff(A[2],n,x)}
%Y Cf. A145085, A145086, A145088, A145089; A145080, A145082.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Oct 01 2008
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