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A160484
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Third right hand column of the Beta triangle A160480
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2
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-299, 2063, -8948, 29034, -77537, 180137, -376946, 727116, -1314087, 2251475, -3689600, 5822654, -8896509, 13217165, -19159838, 27178688, -37817187, 51719127, -69640268, 92460626, -121197401, 157018545, -201256970, 255425396
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history;
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internal format)
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OFFSET
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1,1
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LINKS
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FORMULA
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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)
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MAPLE
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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
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LinearRecurrence[{-7, -21, -35, -35, -21, -7, -1}, {-299, 2063, -8948, 29034, -77537, 180137, -376946}, 30] (* Harvey P. Dale, Jul 23 2021 *)
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CROSSREFS
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A160483 is the second right hand column.
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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