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%I #6 Jun 13 2017 23:38:12
%S 1,1,1,1,2,1,1,4,3,1,1,8,9,4,1,1,18,27,16,5,1,1,46,89,64,25,6,1,1,136,
%T 327,276,125,36,7,1,1,464,1353,1304,665,216,49,8,1,1,1818,6303,6808,
%U 3825,1366,343,64,9,1,1,8122,32953,39320,23977,9246,2513,512,81,10,1
%N Triangle, read by rows, where column k equals column 0 of A113983^(k+1): T(n,k) = [A113983^(k+1)](n-k,0) for n>=k>=0.
%F T(n, k) = A113983(n+1, k) - T(n, k-1).
%e Triangle T begins:
%e 1;
%e 1,1;
%e 1,2,1;
%e 1,4,3,1;
%e 1,8,9,4,1;
%e 1,18,27,16,5,1;
%e 1,46,89,64,25,6,1;
%e 1,136,327,276,125,36,7,1;
%e 1,464,1353,1304,665,216,49,8,1;
%e 1,1818,6303,6808,3825,1366,343,64,9,1;
%e 1,8122,32953,39320,23977,9246,2513,512,81,10,1; ...
%e where A113983(n+1,k) = T(n,k) + T(n,k-1):
%e A113983(6,3) = 43 = T(5,3) + T(5,2) = 16 + 27;
%e A113983(7,3) = 153 = T(6,3) + T(6,2) = 64 + 89;
%e A113983(8,3) = 603 = T(7,3) + T(7,2) = 276 + 327.
%o (PARI) T(n,k)=local(A,B);A=Mat(1);for(m=2,n+1,B=matrix(m,m); for(i=1,m, for(j=1,i,if(i<3 || j==1 || j==i,B[i,j]=1, B[i,j]=A[i-1,j-1]+(A^2)[i-2,j-1] );));A=B);(A^(k+1))[n-k+1,1]
%Y Cf. A113983, A113988, A113989 (column 1), A113994 (column 2), A113995 (column 3), A113996 (column 4), A113997 (row sums).
%K nonn,tabl
%O 0,5
%A _Paul D. Hanna_, Nov 12 2005
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