OFFSET
0,4
COMMENTS
Column k equals 3^k multiplied by column 0 (A111844) when ignoring zeros above the diagonal.
FORMULA
T(n, k) = 3^k*T(n-k, 0) = 3^k*A111844(n-k) for n>=k>=0.
EXAMPLE
Matrix log of A111840, with factorial denominators, begins:
0;
1/1!, 0;
3/2!, 3/1!, 0;
27/3!, 9/2!, 9/1!, 0;
486/4!, 81/3!, 27/2!, 27/1!, 0;
7776/5!, 1458/4!, 243/3!, 81/2!, 81/1!, 0;
-2423196/6!, 23328/5!, 4374/4!, 729/3!, 243/2!, 243/1!, 0;
PROG
(PARI) T(n, k, q=3)=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