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

0,4

Links

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

Wikipedia, Permutation

Formula

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

Example

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).

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 *)

Crossrefs

Row maxima of A143947.

Cf. A368678.

Sequence in context: A357901 A342056 A363199 * A293031 A255487 A077622

Adjacent sequences: A367591 A367592 A367593 * A367595 A367596 A367597

Keyword

nonn

Author

Alois P. Heinz, Jan 03 2024

Status

approved