A111833 Matrix log of triangle A111830, which shifts columns left and up under matrix 7th power; these terms are the result of multiplying each element in row n and column k by (n-k)!.

0, 1, 0, -5, 7, 0, 83, -35, 49, 0, 16110, 581, -245, 343, 0, -40097784, 112770, 4067, -1715, 2401, 0, -388036363380, -280684488, 789390, 28469, -12005, 16807, 0, 82804198261002036, -2716254543660, -1964791416, 5525730, 199283, -84035, 117649, 0

Offset

0,4

Comments

Column k equals 7^k multiplied by column 0 (A111834) when ignoring zeros above the diagonal.

Links

Table of n, a(n) for n=0..35.

Formula

T(n, k) = 7^k*T(n-k, 0) = A111834(n-k) for n>=k>=0.

Example

Matrix log of A111830, with factorial denominators, begins:
0;
1/1!, 0;
-5/2!, 7/1!, 0;
83/3!, -35/2!, 49/1!, 0;
16110/4!, 581/3!, -245/2!, 343/1!, 0;
-40097784/5!, 112770/4!, 4067/3!, -1715/2!, 2401/1!, 0; ...

Prog

(PARI) T(n, k, q=7)=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

Cf. A111830, A111834 (column 0); log matrices: A110504 (q=-1), A111813 (q=2), A111815 (q=3), A111818 (q=4), A111823 (q=5), A111828 (q=6), A111838 (q=8).

Sequence in context: A021950 A072417 A133412 * A011378 A329346 A258716

Adjacent sequences: A111830 A111831 A111832 * A111834 A111835 A111836

Keyword

frac,sign,tabl

Author

Gottfried Helms and Paul D. Hanna, Aug 22 2005

Status

approved