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%I #7 Jun 22 2016 22:58:12
%S 1,8,136,6232,854848,373259224,540477342400,2672052251004112,
%T 46088422295844824512,2819594595499446574537112,
%U 619804662273405542773923781504,494669890490702036481614523776214128,1445689562032160359098054773761542867676352,15582205179106128515694061249394708070061006521840,623164384826393004269624677225320058520632702496162024576,92950754406669433360560292231532867334028809841256765779355298464,51944751631411703759398930923077536382840396924192243346470672357124333952
%N Column 0 of matrix 8th power of triangle A134049; a(n) = [A134049^8](n,0) = A134049(n+3,3)/8^n.
%H Paul D. Hanna, <a href="/A134053/b134053.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)) );M[n+4,4]/8^n}
%o for(n=0, 20, print1(a(n), ", "))
%Y Cf. A134049; columns: A134050, A134051, A134052; A134054 (row sums).
%K nonn
%O 0,2
%A _Paul D. Hanna_, Oct 04 2007
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