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A090448
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Fourth column (m=3) of triangle A090447.
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5
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9, 96, 500, 1800, 5145, 12544, 27216, 54000, 99825, 174240, 290004, 463736, 716625, 1075200, 1572160, 2247264, 3148281, 4332000, 5865300, 7826280, 10305449, 13406976, 17250000, 21970000, 27720225, 34673184, 43022196, 52983000, 64795425, 78725120, 95065344
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OFFSET
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3,1
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LINKS
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FORMULA
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a(n) = (n^3*(n-1)^2*(n-2)^1)/(1!*2!*3!) for n >= 3.
a(n) = (n^6-4*n^5+5*n^4-2*n^3)/12.
G.f.: -x^3*(x^3+17*x^2+33*x+9)/(x-1)^7. (End)
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). - Wesley Ivan Hurt, May 04 2021
Sum_{n>=3} 1/a(n) = 207/4 - 9*Pi^2/2 - 6*zeta(3).
Sum_{n>=3} (-1)^(n+1)/a(n) = 165/4 - Pi^2/4 - 48*log(2) - 9*zeta(3)/2. (End)
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MAPLE
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MATHEMATICA
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a[n_] := Product[Binomial[n, k], {k, 0, 3}]; Array[a, 30, 3] (* Amiram Eldar, Sep 08 2022 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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