OFFSET
0,4
COMMENTS
Column k equals 4^k multiplied by column 0 (A111849) when ignoring zeros above the diagonal.
FORMULA
T(n, k) = 4^k*T(n-k, 0) = 4^k*A111844(n-k) for n>=k>=0.
EXAMPLE
Matrix log of A111845, with factorial denominators, begins:
0;
1/1!, 0;
4/2!, 4/1!, 0;
56/3!, 16/2!, 16/1!, 0;
1728/4!, 224/3!, 64/2!, 64/1!, 0;
-45696/5!, 6912/4!, 896/3!, 256/2!, 256/1!, 0; ...
PROG
(PARI) L(n, k, q=4)=local(A=Mat(1), B); if(n<k || k<0, 0, for(m=1, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i, B[i, j]=1, if(j==1, B[i, j]=(A^q)[i-1, 1], B[i, j]=(A^q)[i-1, j-1])); )); A=B); B=sum(i=1, #A, -(A^0-A)^i/i); return((n-k)!*B[n+1, k+1]))
CROSSREFS
KEYWORD
AUTHOR
Paul D. Hanna, Aug 23 2005
STATUS
approved