%I #5 Jun 22 2016 22:41:03
%S 1,2,8,80,2225,184700,48156025,41008196507,117576923431865,
%T 1162187460377703220,40342092016795699709297,
%U 4989979910857539524339725455,2225169577804416081963640015838617,3611404965468239375529128539282974032063,21500912257369373138838006883103647202061119889,472700949365256437455861341996789835116478103190166869,38594839432514958712997836406329517947410813633064955364162609,11760334792404044930820367474465749383281197807007630470152427553813828
%N Row sums of triangle A134049.
%H Paul D. Hanna, <a href="/A134054/b134054.txt">Table of n, a(n) for n = 0..40</a>
%e Triangle T=A134049 has the following properties:
%e (1) [T^(2^m)](n,k) = T(n+m,k+m)/(2^m)^(n-k) for m>=0; and
%e (2) [T^( 1/2^(n-1) )](n,k) = (2^k)^(n-k) for n>=k>=0.
%o (PARI) {a(n)=local(M=Mat(1),L,R);for(i=1,n+3, L=sum(j=1,#M,-(M^0-M)^j/j);M=sum(j=0,#L,(L/2^(#L-1))^j/j!); R=matrix(#M+1,#M+1,r,c,if(r>=c,if(r<=#M,M[r,c],2^((c-1)*(#M+1-c))))); M=R^(2^(#R-2)) );sum(k=0,n,M[n+1,k+1])}
%o for(n=0,20,print1(a(n),", "))
%Y Cf. A134049; columns: A134050, A134051, A134052, A134053.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Oct 04 2007