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

Author

Emeric Deutsch, May 28 2008

Keywords

• nonn
• easy

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.

Crossrefs

Cf. A000142, A140711.

Programs

GAP

List([1..30], n -> Factorial(n-1)*(n-1)*(n^2 +13*n+6)/36); # G. C. Greubel, Nov 28 2018

Magma

[Factorial(n-1)*(n-1)*(n^2+13*n+6)/36: n in [1..20]]; // G. C. Greubel, Nov 28 2018

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 *)

PARI

a(n)=(n^2+13*n+6)*(n-1)*(n-1)!/36 \\ Charles R Greathouse IV, Oct 31 2011

Sage

[factorial(n-1)*(n-1)*(n^2 +13*n+6)/36 for n in (1..20)] # G. C. Greubel, Nov 28 2018

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