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%I #16 Apr 21 2022 05:24:55
%S 0,0,0,2,16,108,864,7200,69120,705600,8064000,97977600,1306368000,
%T 18441561600,281652940800,4533271142400,78111748915200,
%U 1412288317440000,27115935694848000,544201764986880000,11524272670310400000,254238259854458880000,5887622859787468800000
%N Total number of consecutive triples of the form (odd, even, odd) or (even, odd, even) in all permutations of [n].
%C All terms are even.
%H Alois P. Heinz, <a href="/A329550/b329550.txt">Table of n, a(n) for n = 0..449</a>
%F a(n) = Sum_{k>=1} k * A152877(n,k).
%F a(n) ~ n! * n / 4. - _Vaclav Kotesovec_, Nov 19 2019
%e a(3) = 2: 123, 321.
%p a:= proc(n) option remember; `if`(n<5, [0$3, 2, 16][n+1],
%p (n-2)*(2*(n-4)*a(n-1)+(n-3)^2*n*a(n-2))/(n-3)/(n-4))
%p end:
%p seq(a(n), n=0..30);
%t a[n_] := a[n] = If[n < 5, {0, 0, 0, 2, 16}[[n+1]],
%t (n-2)*(2*(n-4)*a[n-1] + (n-3)^2*n*a[n-2])/(n-3)/(n-4)];
%t Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Apr 21 2022, after _Alois P. Heinz_ *)
%Y Cf. A152877.
%K nonn
%O 0,4
%A _Alois P. Heinz_, Nov 16 2019
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