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

1, 1, 2, 1, 5, 6, 1, 9, 25, 26, 1, 14, 67, 149, 150, 1, 20, 145, 525, 1081, 1082, 1, 27, 275, 1450, 4651, 9365, 9366, 1, 35, 476, 3430, 15421, 47229, 94585, 94586, 1, 44, 770, 7266, 43281, 180894, 545707, 1091669, 1091670, 1, 54, 1182, 14154, 107751, 581280, 2359225, 7087005, 14174521, 14174522

Offset: 1

Author

N. J. A. Sloane, Apr 22 2014

Keywords

• nonn
• tabl

Comments

Steffensen's bracket function [n,k] = Sum_{s=k..n-1} Stirling2(n,s+1)*s!/k!.

The numbers are used in numerical integration.

Examples

			Triangle begins:
1,
1, 2,
1, 5, 6,
1, 9, 25, 26,
1, 14, 67, 149, 150,
1, 20, 145, 525, 1081, 1082,
1, 27, 275, 1450, 4651, 9365, 9366,
1, 35, 476, 3430, 15421, 47229, 94585, 94586,
1, 44, 770, 7266, 43281, 180894, 545707, 1091669, 1091670,
...
		

References

• J. F. Steffensen, On a class of polynomials and their application to actuarial problems, Skandinavisk Aktuarietidskrift, 11 (1928), 75-97.

Links

• J. F. Steffensen, On a class of polynomials and their application to actuarial problems, Skandinavisk Aktuarietidskrift, Vol. 11, pp. 75-97, 1928.

Crossrefs

Diagonals include A000096, A000629, A002050, A002051, A241169, A241170.

Programs

Maple

with(combinat);
T:=proc(n,k) add(stirling2(n,s+1)*s!/k!,s=k..n-1); end;
for n from 1 to 12 do lprint([seq(T(n,n-k),k=1..n)]); od: