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A262745 Number of permutations of [n] with an odd number of rises. 2
0, 0, 1, 4, 12, 52, 360, 2656, 20160, 177472, 1814400, 20135296, 239500800, 3102326272, 43589145600, 654789062656, 10461394944000, 177738781376512, 3201186852864000, 60837094646972416, 1216451004088320000, 25542995336828157952, 562000363888803840000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..400

FORMULA

E.g.f.: (1/(1-x) -1 -tanh(x))/2.

a(n) = A000142(n) - A128103(n).

EXAMPLE

a(2) = 1: 12.

a(3) = 4: 132, 213, 231, 312.

MAPLE

b:= proc(u, o, t) option remember; `if`(u+o=0, t,

      add(b(u-j, o+j-1, t), j=1..u)+

      add(b(u+j-1, o-j, 1-t), j=1..o))

    end:

a:= n-> b(n, 0$2):

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

MATHEMATICA

b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, t,

     Sum[b[u - j, o + j - 1, t], {j, 1, u}] +

     Sum[b[u + j - 1, o - j, 1 - t], {j, 1, o}]];

a[n_] := b[n, 0, 0];

Table[a[n], {n, 0, 25}] (* Jean-Fran├žois Alcover, Nov 01 2021, after Alois P. Heinz *)

CROSSREFS

Cf. A000142, A128103.

Sequence in context: A065525 A317281 A190342 * A180381 A149413 A149414

Adjacent sequences:  A262742 A262743 A262744 * A262746 A262747 A262748

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 29 2015

STATUS

approved

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Last modified November 29 12:24 EST 2021. Contains 349416 sequences. (Running on oeis4.)