A241169 Steffensen's bracket function [n,3].

0, 0, 0, 1, 14, 145, 1450, 15421, 180894, 2359225, 34072850, 540848341, 9363767974, 175619185105, 3547113529050, 76761061273261, 1771884886830254, 43456922321543785, 1128511554354422050, 30933862439582514181, 892562598747547111734, 27041608332832948251265, 858281473267724898703850

Offset: 1

Author

N. J. A. Sloane, Apr 22 2014

Keywords

• nonn

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

A diagonal of the triangular array in A241168.

Programs

Maple

with(combinat);
T:=proc(n,k) add(stirling2(n,s+1)*s!/k!,s=k..n-1); end;
[seq(T(n,3),n=1..16)];

Mathematica

Flatten[{0,0,0,Table[Sum[StirlingS2[n, s+1]*s!/3!, {s,3,n-1}],{n,4,20}]}] (* Vaclav Kotesovec, Apr 22 2014 *)

Formula

See A241168.

a(n) ~ (n-1)! / (6*(log(2))^n). - Vaclav Kotesovec, Apr 22 2014