A160484 Third right hand column of the Beta triangle A160480.
-299, 2063, -8948, 29034, -77537, 180137, -376946, 727116, -1314087, 2251475, -3689600, 5822654, -8896509, 13217165, -19159838, 27178688, -37817187, 51719127, -69640268, 92460626, -121197401, 157018545, -201256970, 255425396
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (-7,-21,-35,-35,-21,-7,-1).
Programs
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Maple
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);
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Mathematica
LinearRecurrence[{-7,-21,-35,-35,-21,-7,-1},{-299,2063,-8948,29034,-77537,180137,-376946},30] (* Harvey P. Dale, Jul 23 2021 *)
Formula
From Chai Wah Wu, Sep 24 2020: (Start)
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.
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)