OFFSET
0,5
COMMENTS
Column k equals 2^k multiplied by column 0 (A111979) when ignoring zeros above the diagonal.
FORMULA
T(n, k) = 2^k*T(n-k, 0) = 2^k*A111979(n-k) for n>=k>=0.
EXAMPLE
Matrix log of A111975, with factorial denominators, begins:
0;
1/1!, 0;
0/2!, 2/1!, 0;
16/3!, 0/2!, 4/1!, 0;
0/4!, 32/3!, 0/2!, 8/1!, 0;
1536/5!, 0/4!, 64/3!, 0/2!, 16/1!, 0;
0/6!, 3072/5!, 0/4!, 128/3!, 0/2!, 32/1!, 0;
-319488/7!, 0/6!, 6144/5!, 0/4!, 256/3!, 0/2!, 64/1!, 0; ...
PROG
(PARI) T(n, k, q=2)=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]=if(i>2, (A^q)[i-1, 2], 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 25 2005
STATUS
approved