A368678 Number of permutations of [n] whose cycle maxima sum to 2n.

1, 0, 0, 1, 2, 10, 41, 260, 1552, 12818, 101280, 1021908, 10154064, 121656672, 1447205472, 20215013184, 280271024640, 4457067906240, 70826580095040, 1264147627392000, 22588177271650560, 448332829478760960, 8899910723677639680, 194096853444946636800

Offset: 0

Author

Alois P. Heinz, Jan 02 2024

Keywords

• nonn

Examples

			a(0) = 1: the empty permutation.
a(3) = 1: (1)(2)(3).
a(4) = 2: (1)(23)(4), (1)(24)(3).
a(5) = 10: (12)(3)(45), (13)(2)(45), (1)(234)(5), (1)(243)(5), (1)(235)(4),
  (1)(253)(4), (145)(2)(3), (154)(2)(3), (1)(24)(35), (1)(25)(34).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..451
• Wikipedia, Permutation

Crossrefs

Cf. A143947, A367594, A368246, A368675.

Programs

Maple

b:= proc(n) option remember;
      `if`(n=0, 1, expand(b(n-1)*(t-n+x^n)))
    end:
a:= n-> coeff(subs(t=n, b(n)), x, 2*n):
seq(a(n), n=0..23);

Mathematica

T[n_] := Module[{t}, CoefficientList[Product[n-k+t^k, {k, 1, n-1}]*t^(n-1), t]];
a[n_] := Switch[n, 0, 1, 1|2, 0, _, T[n][[2 n]]];
Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Oct 03 2024 *)

Formula

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