cp's OEIS Frontend

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

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