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%I #15 Sep 08 2022 08:45:34
%S 0,1,6,37,256,2000,17520,170520,1827840,21409920,272160000,3732220800,
%T 54925516800,863480217600,14442536908800,256086230400000,
%U 4798293147648000,94731418349568000,1965528727658496000
%N Number of white corners in all permutations of {1,2,...,n} (for definition see the Eriksson-Linusson references).
%D K. Eriksson and S. Linusson. Combinatorics of Fulton's essential set. Duke Mathematical Journal 85(1):61-76, 1996.
%H G. C. Greubel, <a href="/A140712/b140712.txt">Table of n, a(n) for n = 1..445</a>
%H K. Eriksson and S. Linusson, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v2i1r6">The size of Fulton's essential set</a>, Electronic J. Combinatorics, Vol. 2, #R6, 1995.
%H K. Eriksson and S. Linusson, <a href="https://www.researchgate.net/publication/2550835_Combinatorics_of_Fulton's_essential_set">Combinatorics of Fulton's essential set</a>, ResearchGate, 1998.
%F a(n) = Sum_{k=0..n-1} k*A140711(n,k).
%F a(n) = (n-1)!*(binomial(n-1,3)+6*binomial(n,2)])/6 = (n-1)!*(n-1)*(n^2 +13*n+6)/36.
%F 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
%F 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
%p seq((1/36)*(n-1)*factorial(n-1)*(n^2+13*n+6),n=1..20);
%t Table[(n-1)!*(n-1)*(n^2 +13*n+6)/36, {n,1,20}] (* _G. C. Greubel_, Nov 28 2018 *)
%o (PARI) a(n)=(n^2+13*n+6)*(n-1)*(n-1)!/36 \\ _Charles R Greathouse IV_, Oct 31 2011
%o (Magma) [Factorial(n-1)*(n-1)*(n^2+13*n+6)/36: n in [1..20]]; // _G. C. Greubel_, Nov 28 2018
%o (Sage) [factorial(n-1)*(n-1)*(n^2 +13*n+6)/36 for n in (1..20)] # _G. C. Greubel_, Nov 28 2018
%o (GAP) List([1..30], n -> Factorial(n-1)*(n-1)*(n^2 +13*n+6)/36); # _G. C. Greubel_, Nov 28 2018
%Y Cf. A000142, A140711.
%K nonn,easy
%O 1,3
%A _Emeric Deutsch_, May 28 2008
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