A329550 Total number of consecutive triples of the form (odd, even, odd) or (even, odd, even) in all permutations of [n].

0, 0, 0, 2, 16, 108, 864, 7200, 69120, 705600, 8064000, 97977600, 1306368000, 18441561600, 281652940800, 4533271142400, 78111748915200, 1412288317440000, 27115935694848000, 544201764986880000, 11524272670310400000, 254238259854458880000, 5887622859787468800000

Offset: 0

Author

Alois P. Heinz, Nov 16 2019

Keywords

• nonn

Comments

All terms are even.

Examples

			a(3) = 2: 123, 321.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..449

Crossrefs

Cf. A152877.

Programs

Maple

a:= proc(n) option remember; `if`(n<5, [0$3, 2, 16][n+1],
     (n-2)*(2*(n-4)*a(n-1)+(n-3)^2*n*a(n-2))/(n-3)/(n-4))
    end:
seq(a(n), n=0..30);

Mathematica

a[n_] := a[n] = If[n < 5, {0, 0, 0, 2, 16}[[n+1]],
     (n-2)*(2*(n-4)*a[n-1] + (n-3)^2*n*a[n-2])/(n-3)/(n-4)];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Apr 21 2022, after Alois P. Heinz *)

Formula

a(n) = Sum_{k>=1} k * A152877(n,k).

a(n) ~ n! * n / 4. - Vaclav Kotesovec, Nov 19 2019