OFFSET
1,8
COMMENTS
Many well-known integer sequences arise from such a matrix product of combinatorial coefficients. In the present case we have as the first row A000166 = subfactorial or rencontres numbers, or derangements: number of permutations of n elements with no fixed points.
FORMULA
(In Maple notation:) Matrix product B.A of matrix A[i,j]:=binomial(j-1,i-1) with i = 1 to p+1, j = 1 to p+1, p=8 and of matrix B[i,j]:=stirling1(j,i) with i from 1 to d, j from 1 to d, d=9.
EXAMPLE
Matrix begins:
1 0 1 -2 9 -44 265 -1854 14833
0 1 -1 5 -20 109 -689 5053 -42048
0 0 1 -3 17 -100 694 -5453 48082
0 0 0 1 -6 45 -355 3094 -29596
0 0 0 0 1 -10 100 -1015 10899
0 0 0 0 0 1 -15 196 -2492
0 0 0 0 0 0 1 -21 350
0 0 0 0 0 0 0 1 -28
0 0 0 0 0 0 0 0 1
CROSSREFS
KEYWORD
tabl,sign
AUTHOR
Thomas Wieder, Dec 29 2006
STATUS
approved