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A140712
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Number of white corners in all permutations of {1,2,...,n} (for definition see the Eriksson-Linusson references).
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3
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0, 1, 6, 37, 256, 2000, 17520, 170520, 1827840, 21409920, 272160000, 3732220800, 54925516800, 863480217600, 14442536908800, 256086230400000, 4798293147648000, 94731418349568000, 1965528727658496000
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OFFSET
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1,3
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REFERENCES
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K. Eriksson and S. Linusson. Combinatorics of Fulton's essential set. Duke Mathematical Journal 85(1):61-76, 1996.
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n-1} k*A140711(n,k).
a(n) = (n-1)!*(binomial(n-1,3)+6*binomial(n,2)])/6 = (n-1)!*(n-1)*(n^2 +13*n+6)/36.
E.g.f.: (x*(6 + 3*x - 7*x^2) + (6 - 18*x + 18*x^2 - 6*x^3)*log(1-x))/(36* (1-x)^3). - G. C. Greubel, Nov 28 2018
D-finite with recurrence 2*(-n+5)*a(n) +(2*n^2-31*n+51)*a(n-1) +(25*n-14)*(n-2)*a(n-2)=0. - R. J. Mathar, Jul 26 2022
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MAPLE
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seq((1/36)*(n-1)*factorial(n-1)*(n^2+13*n+6), n=1..20);
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MATHEMATICA
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Table[(n-1)!*(n-1)*(n^2 +13*n+6)/36, {n, 1, 20}] (* G. C. Greubel, Nov 28 2018 *)
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PROG
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(Magma) [Factorial(n-1)*(n-1)*(n^2+13*n+6)/36: n in [1..20]]; // G. C. Greubel, Nov 28 2018
(Sage) [factorial(n-1)*(n-1)*(n^2 +13*n+6)/36 for n in (1..20)] # G. C. Greubel, Nov 28 2018
(GAP) List([1..30], n -> Factorial(n-1)*(n-1)*(n^2 +13*n+6)/36); # G. C. Greubel, Nov 28 2018
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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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