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A241168 Triangle read by rows: T(n,k) (1 <= k <= n) = Steffensen's bracket function [n,n-k].

%I A241168 #18 Jul 27 2015 20:54:17
%S A241168 1,1,2,1,5,6,1,9,25,26,1,14,67,149,150,1,20,145,525,1081,1082,1,27,
%T A241168 275,1450,4651,9365,9366,1,35,476,3430,15421,47229,94585,94586,1,44,
%U A241168 770,7266,43281,180894,545707,1091669,1091670,1,54,1182,14154,107751,581280,2359225,7087005,14174521,14174522
%N A241168 Triangle read by rows: T(n,k) (1 <= k <= n) = Steffensen's bracket function [n,n-k].
%C A241168 Steffensen's bracket function [n,k] = Sum_{s=k..n-1} Stirling2(n,s+1)*s!/k!.
%C A241168 The numbers are used in numerical integration.
%D A241168 J. F. Steffensen, On a class of polynomials and their application to actuarial problems, Skandinavisk Aktuarietidskrift, 11 (1928), 75-97.
%H A241168 J. F. Steffensen, <a href="http://dx.doi.org/10.1080/03461238.1928.10416863">On a class of polynomials and their application to actuarial problems</a>, Skandinavisk Aktuarietidskrift, Vol. 11, pp. 75-97, 1928.
%e A241168 Triangle begins:
%e A241168 1,
%e A241168 1, 2,
%e A241168 1, 5, 6,
%e A241168 1, 9, 25, 26,
%e A241168 1, 14, 67, 149, 150,
%e A241168 1, 20, 145, 525, 1081, 1082,
%e A241168 1, 27, 275, 1450, 4651, 9365, 9366,
%e A241168 1, 35, 476, 3430, 15421, 47229, 94585, 94586,
%e A241168 1, 44, 770, 7266, 43281, 180894, 545707, 1091669, 1091670,
%e A241168 ...
%p A241168 with(combinat);
%p A241168 T:=proc(n,k) add(stirling2(n,s+1)*s!/k!,s=k..n-1); end;
%p A241168 for n from 1 to 12 do lprint([seq(T(n,n-k),k=1..n)]); od:
%Y A241168 Diagonals include A000096, A000629, A002050, A002051, A241169, A241170.
%K A241168 nonn,tabl
%O A241168 1,3
%A A241168 _N. J. A. Sloane_, Apr 22 2014