A367594 Number of permutations of [n] whose cycle maxima sum to k, where k is chosen so as to maximize this number.

1, 1, 1, 2, 7, 27, 142, 834, 5962, 46788, 426708, 4198632, 46516800, 551415936, 7197404976, 99712618560, 1500173940960, 23786129681280, 405087689727360, 7237524061198080, 137652562628778240, 2735042530132523520, 57482464477451489280, 1257272784581092070400

Offset: 0

Author

Alois P. Heinz, Jan 03 2024

Keywords

• nonn

Examples

			a(4) = 7 = A143947(4,7): (123)(4), (132)(4), (124)(3), (142)(3), (13)(24),
  (14)(23), (1)(2)(34).
a(5) = 27 = A143947(5,9): (1234)(5), (1243)(5), (1324)(5), (1342)(5), (1423)(5), (1432)(5), (1235)(4), (1253)(4), (1325)(4), (1352)(4), (1523)(4), (1532)(4), (124)(35), (142)(35), (125)(34), (152)(34), (134)(25), (143)(25), (135)(24), (153)(24), (14)(235), (14)(253), (15)(234), (15)(243), (1)(23)(45), (1)(245)(3), (1)(254)(3).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..400
• Wikipedia, Permutation

Crossrefs

Row maxima of A143947.

Cf. A368678.

Programs

Maple

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

Mathematica

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

Formula

a(n) = A143947(n,2n-1) for n>=1, a(0) = 1.