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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 (list; graph; refs; listen; history; text; internal format)
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

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: A271905 A073013 A192238 * A079751 A088312 A012364

Adjacent sequences:  A140709 A140710 A140711 * A140713 A140714 A140715

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, May 28 2008

STATUS

approved

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Last modified July 24 20:26 EDT 2021. Contains 346273 sequences. (Running on oeis4.)