A140712 Number of white corners in all permutations of {1,2,...,n} (for definition see the Eriksson-Linusson references).

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

G. C. Greubel, Table of n, a(n) for n = 1..445

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

Cf. A000142, A140711.

Sequence in context: A355957 A073013 A192238 * A362094 A079751 A088312

Adjacent sequences: A140709 A140710 A140711 * A140713 A140714 A140715

Keyword

nonn,easy

Author

Emeric Deutsch, May 28 2008

Status

approved