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A227918 Sum over all permutations beginning and ending with ascents, and without double ascents on n elements and each permutation contributes 2 to the power of the number of double descents. 2
1, 0, 5, 22, 137, 956, 7653, 68874, 688745, 7576192, 90914309, 1181886014, 16546404201, 248196063012, 3971137008197, 67509329139346, 1215167924508233, 23088190565656424, 461763811313128485, 9697040037575698182, 213334880826665360009, 4906702259013303280204, 117760854216319278724901 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,3

LINKS

Table of n, a(n) for n=2..24.

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

For n=4 the 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

Cf. A000166, A230071, A055596.

Sequence in context: A111154 A221539 A028561 * A009638 A121942 A006294

Adjacent sequences:  A227915 A227916 A227917 * A227919 A227920 A227921

KEYWORD

nonn

AUTHOR

Richard Ehrenborg, Oct 08 2013

STATUS

approved

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Last modified October 17 16:51 EDT 2019. Contains 328120 sequences. (Running on oeis4.)