OFFSET
0,5
COMMENTS
Column k equals 2^k multiplied by column 0 (A111814) when ignoring zeros above the diagonal.
FORMULA
T(n, k) = 2^k*T(n-k, 0) = A111814(n-k) for n>=k>=0.
EXAMPLE
Matrix log of A078121, with factorial denominators, begins:
0;
1/1!, 0;
0/2!, 2/1!, 0;
-2/3!, 0/2!, 4/1!, 0;
0/4!, -4/3!, 0/2!, 8/1!, 0;
216/5!, 0/4!, -8/3!, 0/2!, 16/1!, 0;
0/6!, 432/5!, 0/4!, -16/3!, 0/2!, 32/1!, 0;
-568464/7!, 0/6!, 864/5!, 0/4!, -32/3!, 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 || j==1, B[i, j]=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
Gottfried Helms and Paul D. Hanna, Aug 22 2005
STATUS
approved