A241170 Steffensen's bracket function [n,n-3].

6, 25, 67, 145, 275, 476, 770, 1182, 1740, 2475, 3421, 4615, 6097, 7910, 10100, 12716, 15810, 19437, 23655, 28525, 34111, 40480, 47702, 55850, 65000, 75231, 86625, 99267, 113245, 128650, 145576, 164120, 184382, 206465, 230475, 256521, 284715, 315172

Offset: 3

Author

N. J. A. Sloane, Apr 22 2014

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 3..1000
• Margaret Bayer, Mark Denker, Marija Jelić Milutinović, Sheila Sundaram, and Lei Xue, Topology of Cut Complexes II, arXiv:2407.08158 [math.CO], 2024. See p. 15.
• J. F. Steffensen, On a class of polynomials and their application to actuarial problems, Skandinavisk Aktuarietidskrift, Vol. 11, pp. 75-97, 1928.
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

A diagonal of the triangular array in A241168.

Programs

Magma

[(n-2)*(n-1)*(24+7*n+3*n^2)/24: n in [3..50]]; // Vincenzo Librandi, Dec 12 2014

Magma

I:=[6,25,67,145,275]; [n le 5 select I[n] else 5*Self(n-1)-10*Self(n-2)+10*Self(n-3)-5*Self(n-4)+Self(n-5): n in [1..50]]; // Vincenzo Librandi, Dec 12 2014

Maple

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

Mathematica

Table[(n-2)*(n-1)*(24 + 7*n + 3*n^2)/24,{n,3,20}] (* Vaclav Kotesovec, Apr 23 2014 *)
CoefficientList[Series[(6 - 5 x + 2 x^2) / (1 - x)^5, {x, 0, 50}], x] (* Vincenzo Librandi, Dec 12 2014 *)

PARI

for(n=3,30, print1((n-2)*(n-1)*(24+7*n+3*n^2)/24, ", ")) \\ G. C. Greubel, Feb 07 2018

Formula

See A241168.

a(n) = (n-2)*(n-1)*(24 + 7*n + 3*n^2)/24. - Vaclav Kotesovec, Apr 23 2014

From Vincenzo Librandi, Dec 12 2014: (Start)

G.f.: x^3*(6-5*x+2*x^2)/(1-x)^5.

a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5) for n>4.(End)