A200142 Number of near-matchings on the complete graph over 2n+1 vertices.

3, 30, 315, 3780, 51975, 810810, 14189175, 275675400, 5892561675, 137493105750, 3478575575475, 94870242967500, 2774954606799375, 86663966950811250, 2878481759437659375, 101322557932205610000, 3767932623103896121875, 147614301587482048068750

Offset

1,1

Comments

A near-matching on the complete graph over 2n+1 vertices is an edge cover such that all but two edges are pairwise non-adjacent. A001147 corresponds to the number of matchings in even sized complete graphs.

Links

Table of n, a(n) for n=1..18.

Formula

a(n) = (2n+1)! / (2^n * (n-1)!).

a(n) ~ 2^(n+3/2) * n^(n+2) / exp(n). - Amiram Eldar, Jul 12 2026

Mathematica

Table[(2*n + 1)!/(2^n (n - 1)!), {n, 30}] (* T. D. Noe, Nov 15 2011 *)

Crossrefs

Cf. A001147.

Sequence in context: A037659 A131586 A163475 * A339626 A160473 A144283

Adjacent sequences: A200139 A200140 A200141 * A200143 A200144 A200145

Keyword

nonn,changed

Author

Ivo Vigan, Nov 14 2011

Status

approved