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A140712
Number of white corners in all permutations of {1,2,...,n} (for definition see the Eriksson-Linusson references).
3
0, 1, 6, 37, 256, 2000, 17520, 170520, 1827840, 21409920, 272160000, 3732220800, 54925516800, 863480217600, 14442536908800, 256086230400000, 4798293147648000, 94731418349568000, 1965528727658496000
OFFSET
1,3
REFERENCES
K. Eriksson and S. Linusson. Combinatorics of Fulton's essential set. Duke Mathematical Journal 85(1):61-76, 1996.
LINKS
K. Eriksson and S. Linusson, The size of Fulton's essential set, Electronic J. Combinatorics, Vol. 2, #R6, 1995.
K. Eriksson and S. Linusson, Combinatorics of Fulton's essential set, ResearchGate, 1998.
FORMULA
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
MAPLE
seq((1/36)*(n-1)*factorial(n-1)*(n^2+13*n+6), n=1..20);
MATHEMATICA
Table[(n-1)!*(n-1)*(n^2 +13*n+6)/36, {n, 1, 20}] (* G. C. Greubel, Nov 28 2018 *)
PROG
(PARI) a(n)=(n^2+13*n+6)*(n-1)*(n-1)!/36 \\ Charles R Greathouse IV, Oct 31 2011
(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
CROSSREFS
Sequence in context: A355957 A073013 A192238 * A362094 A079751 A088312
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 28 2008
STATUS
approved