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%I #3 Mar 30 2012 18:36:58
%S 1,1,1,1,1,1,1,2,1,1,1,5,4,1,1,1,16,22,8,1,1,1,75,164,92,16,1,1,1,594,
%T 1837,1464,376,32,1,1,1,8420,34176,35190,12336,1520,64,1,1,1,212790,
%U 1106012,1393400,612316,101216,6112,128,1,1,1,9542280,63053480,95005100
%N Triangle T, read by rows, where column k equals column k of T^(2^k) shift down 1 row, with T(n,n)=T(n+1,n)=1 for n>=0.
%e Triangle begins:
%e 1;
%e 1, 1;
%e 1, 1, 1;
%e 1, 2, 1, 1;
%e 1, 5, 4, 1, 1;
%e 1, 16, 22, 8, 1, 1;
%e 1, 75, 164, 92, 16, 1, 1;
%e 1, 594, 1837, 1464, 376, 32, 1, 1;
%e 1, 8420, 34176, 35190, 12336, 1520, 64, 1, 1;
%e 1, 212790, 1106012, 1393400, 612316, 101216, 6112, 128, 1, 1; ...
%e where column 0 of T^(2^0) equals column 0 of T.
%e The matrix square T^2 begins:
%e 1;
%e 2, 1;
%e 3, 2, 1;
%e 5, 5, 2, 1;
%e 12, 16, 9, 2, 1;
%e 49, 75, 56, 17, 2, 1;
%e 350, 594, 506, 208, 33, 2, 1; ...
%e where column 1 of T^(2^1) equals column 1 of T.
%e The matrix 4th power T^4 begins:
%e 1;
%e 4, 1;
%e 10, 4, 1;
%e 26, 14, 4, 1;
%e 93, 60, 22, 4, 1;
%e 525, 379, 164, 38, 4, 1;
%e 4940, 3918, 1837, 516, 70, 4, 1; ...
%e where column 2 of T^(2^2) equals column 2 of T.
%o (PARI) {T(n, k)=local(A=Mat(1), B); for(m=1, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i, B[i, j]=1, B[i, j]=(A^(2^(j-1)))[i-1, j]); )); A=B); return(A[n+1, k+1])}
%Y Cf. A121396 (column 1), A121397 (column 2).
%K nonn,tabl
%O 0,8
%A _Paul D. Hanna_, Jul 27 2006
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