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A228614 Number of permutations of [n] having a shortest ascending run of length one. 4
0, 1, 1, 5, 18, 101, 611, 4452, 36287, 333395, 3382758, 37688597, 456839351, 5989023768, 84421235807, 1273482972215, 20470309460322, 349326503482301, 6307682420743595, 120157254334350828, 2408293016265606623, 50663563124372167787, 1116225038923857181614 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

a(n) = A000142(n) - A097899(n).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

FORMULA

E.g.f.: 1/(1-x) - sqrt(3)*exp(-x/2) / (2*cos(sqrt(3)*x/2+Pi/6)).

EXAMPLE

a(1) = 1: 1.

a(2) = 1: 21.

a(3) = 5: 132, 213, 231, 312, 321.

a(4) = 18: 1243, 1342, 1432, 2134, 2143, 2341, 2431, 3124, 3142, 3214, 3241, 3421, 4123, 4132, 4213, 4231, 4312, 4321.

MAPLE

g:= proc(u, o) option remember; `if`(u+o<2, u,

      add(b(u-i, o+i-1), i=1..u) +add(g(u+i-1, o-i), i=1..o))

    end:

b:= proc(u, o) option remember; `if`(u+o<2, 1-o,

      u*(u+o-1)! +add(g(u+i-1, o-i), i=1..o))

    end:

a:= n-> add(b(j-1, n-j), j=1..n):

seq(a(n), n=0..25);

CROSSREFS

Column k=1 of A064315.

Sequence in context: A188329 A165962 A127756 * A158455 A009442 A332784

Adjacent sequences:  A228611 A228612 A228613 * A228615 A228616 A228617

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 27 2013

STATUS

approved

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Last modified September 28 17:43 EDT 2020. Contains 337393 sequences. (Running on oeis4.)