%I A126353
%S A126353 1,1,0,1,1,1,1,3,5,2,1,6,17,20,9,1,10,45,100,109,44,1,15,100,355,694,
%T A126353 689,265,1,21,196,1015,3094,5453,5053,1854,1,28,350,2492,10899,29596,
%U A126353 48082,42048,14833
%V A126353 1,1,0,1,-1,1,1,-3,5,-2,1,-6,17,-20,9,1,-10,45,-100,109,-44,1,-15,100,
-355,694,-689,
%W A126353 265,1,-21,196,-1015,3094,-5453,5053,-1854,1,-28,350,-2492,10899,-29596,
48082,-42048,
%X A126353 14833
%N A126353 Triangle read by rows: matrix product of the Stirling numbers of the
first kind with the binomial coefficients.
%C A126353 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.
%H A126353 Thomas Wieder, <a href="http://www.thomas-wieder.privat.t-online.de/">
Home Page</a>.
%H A126353 Thomas Wieder, <a href="http://homepages.tu-darmstadt.de/~wieder">(Old)
Home Page</a>.
%F A126353 (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.
%e A126353 Matrix begins:
%e A126353 1 0 1 -2 9 -44 265 -1854 14833
%e A126353 0 1 -1 5 -20 109 -689 5053 -42048
%e A126353 0 0 1 -3 17 -100 694 -5453 48082
%e A126353 0 0 0 1 -6 45 -355 3094 -29596
%e A126353 0 0 0 0 1 -10 100 -1015 10899
%e A126353 0 0 0 0 0 1 -15 196 -2492
%e A126353 0 0 0 0 0 0 1 -21 350
%e A126353 0 0 0 0 0 0 0 1 -28
%e A126353 0 0 0 0 0 0 0 0 1
%Y A126353 Cf. A039810, A039814, A126350, A126351, A054654.
%Y A126353 Sequence in context: A140735 A161865 A145325 this_sequence A094791 A115406
A059246
%Y A126353 Adjacent sequences: A126350 A126351 A126352 this_sequence A126354 A126355
A126356
%K A126353 tabl,sign
%O A126353 1,8
%A A126353 Thomas Wieder (thomas.wieder(AT)t-online.de), Dec 29 2006
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