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%I #6 Jul 19 2016 11:21:02
%S 1,3,21,243,4029,88491,2450085,82648611,3313381293,154912893243,
%T 8322387603093,507658268093811,34817646211022301,2662987196578490187,
%U 225556061819586894597,21030571231219899162435
%N Row 3 of square table A145080.
%C Let R(n,x) be the e.g.f. of row n of square table A145080, then the
%C e.g.f.s satisfy: R(n,x) = exp( n*Integral R(n+1,x) dx ) for n>=1.
%F E.g.f.: A(x) = R(3,x) = exp( 3*Integral R(4,x) dx ) where R(n,x) is the e.g.f. of row n of square table A145080.
%F E.g.f.: A(x) = G(x)^3 where G(x) is the e.g.f. of A145088, which is row 3 of square table A145085.
%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],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]^3,n,x)
%o (PARI) a(n)=local(A=1); for(k=0, n-1, A=exp(intformal((n-k+2)*(A+x*O(x^n))))); n!*polcoeff(A, n)
%o for(n=0, 20, print1(a(n), ", ")) \\ _Paul D. Hanna_, Jan 08 2014
%Y Cf. A145080, A145081, A145082, A145084, A145085, A145088.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Oct 01 2008
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