%I #3 Mar 30 2012 18:37:15

%S 1,1,5,49,741,15457,416661,13908049,557865765,26296627233,

%T 1431946482453,88859040485585,6214831383604709,485449303578082273,

%U 42025472165413172501,4005872618389765500113,418072369437989483917349

%N Row 3 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(3,x) = exp( Integral S(4,x)^4 dx ) where S(n,x) is the e.g.f. of row n of square table A145085.

%F E.g.f.: A(x) = R(3,x)^(1/3) = exp( Integral R(4,x) dx ) where R(3,x) = e.g.f. of A145083 and R(4,x) = e.g.f. of A145084.

%o (PARI) {a(n)=local(A=vector(n+4,j,1+j*x)); for(i=0,n+3,for(j=0,n,m=n+3-j;A[m]=exp(m*intformal(A[m+1]+x*O(x^n))))); n!*polcoeff(A[3]^(1/3),n,x)}

%o (PARI) {a(n)=local(A=vector(n+4,j,1+j*x)); for(i=0,n+3,for(j=0,n,m=n+3-j;A[m]=exp(intformal(A[m+1]^(m+1)+x*O(x^n))))); n!*polcoeff(A[3],n,x)}

%Y Cf. A145085, A145086, A145087, A145089; A145080, A145083.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 01 2008