A163933 Third right hand column of triangle A163932.

11, 105, 510, 1750, 4830, 11466, 24360, 47520, 86625, 149435, 246246, 390390, 598780, 892500, 1297440, 1844976, 2572695, 3525165, 4754750, 6322470, 8298906, 10765150, 13813800, 17550000, 22092525, 27574911, 34146630, 41974310

Offset: 3

Author

Johannes W. Meijer, Aug 13 2009

Keywords

• easy
• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 3..999
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A048994 (Stirling1).

Equals the third right hand column of triangle A163932.

A000217 and A006011 are the first and second right hand columns.

Programs

Maple

nmax:=30; with(combinat, stirling1): for n from 1 to nmax do for m from 1 to n do a(n,m):=(-1)^(n+m)*(m)*(m+1)*stirling1(n+1,m+1)/2 od: od: seq(a(n,n-2),n=3..nmax);

Mathematica

Table[(n-2)(n-1)StirlingS1[n+1,n-1]/2,{n,3,30}] (* Harvey P. Dale, Oct 09 2011 *)

Formula

a(n) = (n-2)*(n-1)*Stirling1(n+1,n-1)/2.

G.f.: z^3*(11 + 6*z^2 + 28*z)/(1-z)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n > 9. - Chai Wah Wu, Jan 25 2021