Ivo Vigan - cp's OEIS frontend

User: Ivo Vigan

Ivo Vigan has authored 2 sequences.

A212553 Irreducible near matchings over 2n+1 vertices.

3, 15, 126, 1395, 18678, 289926, 5090220, 99466371, 2138575590, 50153137650, 1274013771300, 34853264146350, 1021795130252988, 31964591332833900, 1062945070050997656, 37447053359058465507, 1393372283171378001030

Offset: 1

Ivo Vigan, May 20 2012

nonn

			a(1) corresponds to the 3-vertex graphs with edge sets {{1,2},{2,3}}, {{1,2},{1,3}} and {{1,3},{2,3}} respectively.
a(2) corresponds to the 5-vertex graphs with edge sets {{1,2},{2,4},{3,5}}, {{1,4},{2,3},{2,5}} ...

Takahisa Toda and Ivo Vigan, On Separating Convex Points with Lines

Cf. A000699, A200142.

A000699(n)={my(A); A=O(x); for(i=1, n, A=x+A*(2*x*A'-A)); polcoeff(A, n)}
a(n)=A000699(n+1)*(2*n+1)*(n+1)/(2*n);
vector(66,n,a(n))
/* Joerg Arndt, May 27 2012 */

a(n) = A000699(n+1)*(2*n+1)*(n+1)/(2*n).

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

Original entry on oeis.org

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

Offset: 1

Ivo Vigan, Nov 14 2011

nonn

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.

Cf. A001147.

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

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

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User: Ivo Vigan

A212553 Irreducible near matchings over 2n+1 vertices.

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