%I
%S 1,1,0,1,1,1,1,3,5,2,1,6,17,20,9,1,10,45,100,109,44,1,15,100,
%T 355,694,689,265,1,21,196,1015,3094,5453,5053,1854,1,28,350,
%U 2492,10899,29596,48082,42048,14833
%N Triangle read by rows: matrix product of the Stirling numbers of the first kind with the binomial coefficients.
%C Many wellknown 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.
%F (In Maple notation:) Matrix product B.A of matrix A[i,j]:=binomial(j1,i1) 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.
%e Matrix begins:
%e 1 0 1 2 9 44 265 1854 14833
%e 0 1 1 5 20 109 689 5053 42048
%e 0 0 1 3 17 100 694 5453 48082
%e 0 0 0 1 6 45 355 3094 29596
%e 0 0 0 0 1 10 100 1015 10899
%e 0 0 0 0 0 1 15 196 2492
%e 0 0 0 0 0 0 1 21 350
%e 0 0 0 0 0 0 0 1 28
%e 0 0 0 0 0 0 0 0 1
%Y Signed version of A094791 [from _Olivier GĂ©rard_, Jul 31 2011]
%Y Cf. A039810, A039814, A126350, A126351, A054654.
%K tabl,sign
%O 1,8
%A _Thomas Wieder_, Dec 29 2006
