login
Third right hand column of triangle A163932
2

%I #14 Mar 12 2024 02:37:20

%S 11,105,510,1750,4830,11466,24360,47520,86625,149435,246246,390390,

%T 598780,892500,1297440,1844976,2572695,3525165,4754750,6322470,

%U 8298906,10765150,13813800,17550000,22092525,27574911,34146630,41974310

%N Third right hand column of triangle A163932

%H Harvey P. Dale, <a href="/A163933/b163933.txt">Table of n, a(n) for n = 3..999</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

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

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

%F 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

%p 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);

%t Table[(n-2)(n-1)StirlingS1[n+1,n-1]/2,{n,3,30}] (* _Harvey P. Dale_, Oct 09 2011 *)

%Y Cf. A048994 (Stirling1).

%Y Equals the third right hand column of triangle A163932.

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

%K easy,nonn

%O 3,1

%A _Johannes W. Meijer_, Aug 13 2009