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

0,5

Links

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

Wikipedia, Permutation

Formula

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

Example

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).

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);

Crossrefs

Cf. A143947, A367594, A368246, A368675.

Sequence in context: A037561 A135512 A317328 * A083937 A085224 A192695

Adjacent sequences: A368675 A368676 A368677 * A368679 A368680 A368681

Keyword

nonn

Author

Alois P. Heinz, Jan 02 2024

Status

approved