OFFSET
2,3
LINKS
R. Ehrenborg and J. Jung, Descent pattern avoidance, Adv. in Appl. Math., 49 (2012) 375-390.
FORMULA
E.g.f.: (exp(x) - 4 + 4*exp(-x))/(1-x) - 1 + 2*x.
Closest integer to (e - 4 + 4/e)*n! for n > 7.
a(n) = n*a(n-1) + 1 + 4*(-1)^n.
Conjecture: a(n) -n*a(n-1) -a(n-2) +(n-2)*a(n-3) = 0. - R. J. Mathar, Jul 17 2014
EXAMPLE
a(4) = 5 since the sum is over the five permutations 1324, 1423, 2314, 2413 and 3412, and each of them contribute 1 to the sum, since none of them has a double descent.
MATHEMATICA
a[2] = 1; a[n_] := n*a[n - 1] + 1 + 4 (-1)^n; Table[a[n], {n, 2, 20}] (* Wesley Ivan Hurt, May 04 2014 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Richard Ehrenborg, Oct 08 2013
STATUS
approved