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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. 2
1, 1, 4, 60, 2016, 120960, 11404800, 1556755200, 290594304000, 71137485619200, 22117290983424000, 8515157028618240000, 3977233344443842560000, 2215887149047283712000000, 1451849260055780288102400000, 1105220249217462744317952000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

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

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Last modified June 12 13:49 EDT 2021. Contains 344948 sequences. (Running on oeis4.)