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A158471 Stirling-like triangle by rows generated from (x-1)*(x-1)*(x-2)*(x-3)*(x-4)*...

%I A158471 #7 May 04 2019 00:44:09
%S A158471 1,1,-1,1,-2,1,1,-4,5,-2,1,-7,17,-17,6,1,-11,45,-85,74,-24,1,-16,100,
%T A158471 -310,499,-394,120,1,-22,196,-910,2359,-3388,2484,-720,1,-29,350,
%U A158471 -2282,8729,-19901,26200,-18108,5040,1,-37,582,-5082,26985,-89733,185408
%N A158471 Stirling-like triangle by rows generated from (x-1)*(x-1)*(x-2)*(x-3)*(x-4)*...
%C A158471 Row sums of the unsigned triangle = A098558: (1, 2, 4, 12, 48, 240, 1440, 10080, ...).
%F A158471 Triangle read by rows, n-th row = n-th degree polynomial with alternating signs generated from n terms of a*b*c*d*...; where a,b,c,... = (x-1), (x-1), (x-2), (x-3), (x-4), ... n-th row, n > 0 = charpoly of an n X n matrix with (1,1,2,3,4,...) in the diagonal and the rest zeros.
%e A158471 First few rows of the unsigned triangle =
%e A158471 1;
%e A158471 1, 1;
%e A158471 1, 2, 1;
%e A158471 1, 4, 5, 2;
%e A158471 1, 7, 17, 17, 6;
%e A158471 1, 11, 45, 85, 74, 24;
%e A158471 1, 16, 100, 310, 499, 394, 120;
%e A158471 1, 22, 196, 910, 2359, 3388, 2484, 720;
%e A158471 1, 29, 350, 2282, 8729, 19901, 26200, 18108, 5040;
%e A158471 1, 37, 582, 5082, 26985, 89733, 185408, 227708, 149904, 40320;
%e A158471 1, 46, 915, 10320, 72723, 332598, 993005, 1896380, 2199276, 1389456, 362880;
%e A158471 ...
%e A158471 Example: Row 5 = x^5 - 11x^4 + 45x^3 -85x^2 + 74x - 24 =
%e A158471 (x-1)*(x-1)*(x-2)*(x-3)*(x-4).
%Y A158471 Cf. A098558.
%Y A158471 Cf. A103718. - _R. J. Mathar_, Mar 20 2009
%K A158471 tabl,sign
%O A158471 0,5
%A A158471 _Gary W. Adamson_, Mar 20 2009