A351990 Number of minimum edge covers of the complete graph K_n.

0, 1, 3, 3, 30, 15, 315, 105, 3780, 945, 51975, 10395, 810810, 135135, 14189175, 2027025, 275675400, 34459425, 5892561675, 654729075, 137493105750, 13749310575, 3478575575475, 316234143225, 94870242967500, 7905853580625, 2774954606799375, 213458046676875, 86663966950811250, 6190283353629375

Offset

1,3

Links

Table of n, a(n) for n=1..30.

Eric Weisstein's World of Mathematics, Complete Graph

Eric Weisstein's World of Mathematics, Minimum Edge Cover

Formula

a(n) = (n - 1)!! for n == 0 (mod 2).

a(n) = 2^((1 - n)/2)*n!/Gamma((n - 1)/2) for n == 1 (mod 2).

a(1) = 0, a(2) = 1, a(n) = (n - 1)*(((n - 2)*(n - 1)*n - 4)*a(n - 2) - 6*a(n - 1))/(n*(11 + (n - 6)*n) - 10).

Mathematica

Table[Piecewise[{{(2^((1 - n)/2) Gamma[n + 1])/Gamma[(n - 1)/2], Mod[n, 2] == 1}, {(n - 1)!!, Mod[n, 2] == 0}}, 0], {n, 20}]
RecurrenceTable[{a[1] == 0, a[2] == 1, a[n] == ((n - 1) (((n - 2) (n - 1) n - 4) a[n - 2] - 6 a[n - 1]))/(n (11 + (n - 6) n) - 10)}, a, {n, 20}]

Crossrefs

Sequence in context: A139206 A100651 A124244 * A151480 A096351 A367890

Adjacent sequences: A351987 A351988 A351989 * A351991 A351992 A351993

Keyword

nonn

Author

Eric W. Weisstein, Feb 27 2022

Status

approved