A160484 - OEIS

%I #9 Jun 02 2025 01:41:09

%S -299,2063,-8948,29034,-77537,180137,-376946,727116,-1314087,2251475,

%T -3689600,5822654,-8896509,13217165,-19159838,27178688,-37817187,

%U 51719127,-69640268,92460626,-121197401,157018545,-201256970,255425396

%N Third right hand column of the Beta triangle A160480.

%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 From _Chai Wah Wu_, Sep 24 2020: (Start)

%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 > 7.

%F G.f.: x*(-24*x^6 - 162*x^5 - 467*x^4 - 744*x^3 - 786*x^2 - 30*x - 299)/(x + 1)^7. (End)

%p nmax:=27; mmax:=nmax: for m from 1 to mmax do BETA(2,m):=0 end do: BETA(2,1):=-1: for n from 3 to nmax do BETA(n,1):=(2*n-3)^2*BETA(n-1,1)-(2*n-4)! end do: for n from 3 to nmax do for m from 2 to mmax do BETA(n,m):=(2*n-3)^2*BETA(n-1,m)-BETA(n-1,m-1) end do end do: for n from 4 to nmax do a(n-3):=BETA(n,n-3) od: seq(a(n), n=1..nmax-3);

%t LinearRecurrence[{-7,-21,-35,-35,-21,-7,-1},{-299,2063,-8948,29034,-77537,180137,-376946},30] (* _Harvey P. Dale_, Jul 23 2021 *)

%Y A160480 is the Beta triangle.

%Y A160483 is the second right hand column.

%K easy,sign

%O 1,1

%A _Johannes W. Meijer_, May 24 2009