A368678 - OEIS

%I #19 Oct 03 2024 07:55:24

%S 1,0,0,1,2,10,41,260,1552,12818,101280,1021908,10154064,121656672,

%T 1447205472,20215013184,280271024640,4457067906240,70826580095040,

%U 1264147627392000,22588177271650560,448332829478760960,8899910723677639680,194096853444946636800

%N Number of permutations of [n] whose cycle maxima sum to 2n.

%H Alois P. Heinz, <a href="/A368678/b368678.txt">Table of n, a(n) for n = 0..451</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>

%F a(n) = A143947(n,2n).

%e a(0) = 1: the empty permutation.

%e a(3) = 1: (1)(2)(3).

%e a(4) = 2: (1)(23)(4), (1)(24)(3).

%e a(5) = 10: (12)(3)(45), (13)(2)(45), (1)(234)(5), (1)(243)(5), (1)(235)(4),

%e   (1)(253)(4), (145)(2)(3), (154)(2)(3), (1)(24)(35), (1)(25)(34).

%p b:= proc(n) option remember;

%p       `if`(n=0, 1, expand(b(n-1)*(t-n+x^n)))

%p     end:

%p a:= n-> coeff(subs(t=n, b(n)), x, 2*n):

%p seq(a(n), n=0..23);

%t T[n_] := Module[{t}, CoefficientList[Product[n-k+t^k, {k, 1, n-1}]*t^(n-1), t]];

%t a[n_] := Switch[n, 0, 1, 1|2, 0, _, T[n][[2 n]]];

%t Table[a[n], {n, 0, 23}] (* _Jean-François Alcover_, Oct 03 2024 *)

%Y Cf. A143947, A367594, A368246, A368675.

%K nonn

%O 0,5

%A _Alois P. Heinz_, Jan 02 2024