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

3,1

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).

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

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 *)

Crossrefs

Cf. A048994 (Stirling1).

Equals the third right hand column of triangle A163932.

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

Sequence in context: A295840 A158470 A372146 * A359987 A377641 A099839

Adjacent sequences: A163930 A163931 A163932 * A163934 A163935 A163936

Keyword

easy,nonn

Author

Johannes W. Meijer, Aug 13 2009

Status

approved