%I #6 Jun 24 2016 17:55:18
%S 1,1,6,201,43668,66109077,734489285949,62046990518394987,
%T 40856017343540753635650,213541017770966830430102394165,
%U 8983171252819461663303882556431558933,3075323479836540410788167824905924319292059454,8645250567095449548452511767536965844811633035624249353,201074029866479927772743140580731863000103296624613890712276689597
%N Column 0 of triangle A274480.
%H Paul D. Hanna, <a href="/A274481/b274481.txt">Table of n, a(n) for n = 0..40</a>
%o (PARI) {T(n, k)=local(M=Mat(1), L, R); for(i=1, n,
%o L=sum(j=1, #M, -(M^0-M)^j/j); M=sum(j=0, #L, (L/3^(#L-1))^j/j!); R=matrix(#M+1, #M+1, r, c,
%o if(r>=c, if(r<=#M, M[r, c], 3^((c-1)*(#M+1-c))))); M=R^(3^(#M-1)) ); M[n+1, k+1]}
%o for(n=0, 20, print1(T(n, 0), ", "))
%Y Cf. A274480.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jun 24 2016