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

%I A192437 #39 Feb 16 2025 08:33:15
%S A192437 -1,1,2,-4,1,9,-44,42,-12,1,272,-3712,11648,-14208,8256,-2496,400,-32,
%T A192437 1,589185,-25108944,259084440,-1129177840,2605908220,-3594554960,
%U A192437 3190117800,-1910146160,795862790,-235146480,49715240,-7517264,803580,-59120,2840,-80,1,16332454526976,-2333280165691392,81808261704974336
%N A192437 Triangle of nonzero (even) coefficients of the matching polynomials for the hypercube graphs Q_n.
%H A192437 Eric Weisstein, <a href="/A192437/b192437.txt">Table of n, a(n) for n = 1..69</a>
%H A192437 Krishnan Balasubramanian, <a href="https://doi.org/10.3390/sym15020557">Topological Indices, Graph Spectra, Entropies, Laplacians, and Matching Polynomials of n-Dimensional Hypercubes</a>, Symmetry (2023) Vol. 15, No. 2, 557.
%H A192437 Per Hakan Lundow, <a href="https://citeseerx.ist.psu.edu/pdf/95fa86b055ef5705dc58443c7b595ba3ff3b95b1">Enumeration of matchings in polygraphs</a>, 1998.
%H A192437 Per Hakan Lundow, <a href="http://abel.math.umu.se/~phl/Mathematica/">GrafPack</a> (Mathematica package). [Broken link]
%H A192437 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HypercubeGraph.html">Hypercube Graph</a>
%H A192437 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MatchingPolynomial.html">Matching Polynomial</a>
%e A192437 mu(Q_1) = -1+x^2,
%e A192437 mu(Q_2) = 2-4*x^2+x^4,
%e A192437 mu(Q_3) = 9-44*x^2+42*x^4-12*x^6+x^8,
%e A192437 so the triangle begins:
%e A192437 -1,  1;
%e A192437 2,  -4,  1;
%e A192437 9, -44, 42, -12, 1;
%Y A192437 For numbers of matchings, see A045310.
%Y A192437 Cf. A302235.
%K A192437 sign,tabf,hard
%O A192437 1,3
%A A192437 _Eric W. Weisstein_, Jul 13 2011