|
Search: id:A111810
|
|
|
| A111810 |
|
Matrix log of triangle A098539, which shifts columns left and up under matrix square; these terms are the result of multiplying each element in row n and column k by (n-k)!. |
|
+0
4
|
|
| 0, 1, 0, 2, 2, 0, 10, 4, 4, 0, 88, 20, 8, 8, 0, 1096, 176, 40, 16, 16, 0, 11856, 2192, 352, 80, 32, 32, 0, -402480, 23712, 4384, 704, 160, 64, 64, 0, -1891968, -804960, 47424, 8768, 1408, 320, 128, 128, 0, 36024603264, -3783936, -1609920, 94848, 17536, 2816, 640, 256, 256, 0
(list; table; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
COMMENT
|
Column k equals 2^k times column 0 (A111811) when ignoring zeros above the diagonal.
|
|
FORMULA
|
T(n, k) = 2^k*T(n-k, 0) = 2^k*A111811(n-k) for n>=k>=0.
|
|
EXAMPLE
|
Matrix log of A098539, with factorial denominators, begins:
0;
1/1!, 0;
2/2!, 2/1!, 0;
10/3!, 4/2!, 4/1!, 0;
88/4!, 20/3!, 8/2!, 8/1!, 0;
1096/5!, 176/4!, 40/3!, 16/2!, 16/1!, 0;
11856/6!, 2192/5!, 352/4!, 80/3!, 32/2!, 32/1!, 0; ...
|
|
PROGRAM
|
(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]=(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
|
Cf. A098539 (triangle), A111811 (column 0), A111813 (variant), A111941 (q=-1), A111843 (q=3), A111848 (q=4).
Adjacent sequences: A111807 A111808 A111809 this_sequence A111811 A111812 A111813
Sequence in context: A009615 A079194 A117739 this_sequence A019265 A117270 A091466
|
|
KEYWORD
|
frac,sign,tabl
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Aug 22 2005
|
|
|
Search completed in 0.002 seconds
|
