A192437 Triangle of nonzero (even) coefficients of the matching polynomials for the hypercube graphs Q_n.

-1, 1, 2, -4, 1, 9, -44, 42, -12, 1, 272, -3712, 11648, -14208, 8256, -2496, 400, -32, 1, 589185, -25108944, 259084440, -1129177840, 2605908220, -3594554960, 3190117800, -1910146160, 795862790, -235146480, 49715240, -7517264, 803580, -59120, 2840, -80, 1, 16332454526976, -2333280165691392, 81808261704974336

Offset: 1

Author

Eric W. Weisstein, Jul 13 2011

Keywords

• sign
• tabf
• hard

Examples

			mu(Q_1) = -1+x^2,
mu(Q_2) = 2-4*x^2+x^4,
mu(Q_3) = 9-44*x^2+42*x^4-12*x^6+x^8,
so the triangle begins:
-1,  1;
2,  -4,  1;
9, -44, 42, -12, 1;
		

Links

• Eric Weisstein, Table of n, a(n) for n = 1..69
• Krishnan Balasubramanian, Topological Indices, Graph Spectra, Entropies, Laplacians, and Matching Polynomials of n-Dimensional Hypercubes, Symmetry (2023) Vol. 15, No. 2, 557.
• Per Hakan Lundow, Enumeration of matchings in polygraphs, 1998.
• Per Hakan Lundow, GrafPack (Mathematica package). [Broken link]
• Eric Weisstein's World of Mathematics, Hypercube Graph
• Eric Weisstein's World of Mathematics, Matching Polynomial

Crossrefs

For numbers of matchings, see A045310.

Cf. A302235.