A322450 Number of permutations of [2n] in which the size of the last cycle is n and the cycles are ordered by increasing smallest elements.

1, 1, 4, 60, 2016, 120960, 11404800, 1556755200, 290594304000, 71137485619200, 22117290983424000, 8515157028618240000, 3977233344443842560000, 2215887149047283712000000, 1451849260055780288102400000, 1105220249217462744317952000000

Offset

0,3

Comments

For n>0, 2*a(n) corresponds to the number of random walk labelings of the n-barbell graph. - Sela Fried, May 19 2023

Links

Alois P. Heinz, Table of n, a(n) for n = 0..250

Sela Fried and Toufik Mansour, Further results on random walk labelings, arXiv:2305.09971 [math.CO], 2023.

Formula

a(n) = (2n)!/(n*(n+1)) for n>0, a(0) = 1.

a(n) = A136125(2n,n).

From Amiram Eldar, Jan 19 2021: (Start)

Sum_{n>=1} 1/a(n) = e/4 + sinh(1)/2.

Sum_{n>=1} (-1)^(n+1)/a(n) = cos(1)/4 + 3*sin(1)/4. (End)

Maple

a:= n-> `if`(n=0, 1, (2*n)!/(n*(n+1))):
seq(a(n), n=0..18);

Mathematica

a[0] = 1; a[n_] := (2*n)!/(n*(n+1)); Array[a, 16, 0] (* Amiram Eldar, Jan 19 2021 *)

Crossrefs

Cf. A136125.

Sequence in context: A211309 A013502 A303286 * A099705 A012488 A181444

Adjacent sequences: A322447 A322448 A322449 * A322451 A322452 A322453

Keyword

nonn

Author

Alois P. Heinz, Dec 08 2018

Status

approved