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A302235 Triangle T(n,k) of the numbers of k-matchings in the n-hypercube graph (0 <= k <= 2^(n-1)).

%I A302235 #14 Feb 16 2025 08:33:53
%S A302235 1,1,1,4,2,1,12,42,44,9,1,32,400,2496,8256,14208,11648,3712,272,1,80,
%T A302235 2840,59120,803580,7517264,49715240,235146480,795862790,1910146160,
%U A302235 3190117800,3594554960,2605908220,1129177840,259084440,25108944,589185,1,192,17376,986240
%N A302235 Triangle T(n,k) of the numbers of k-matchings in the n-hypercube graph (0 <= k <= 2^(n-1)).
%H A302235 Eric W. Weisstein, <a href="/A302235/b302235.txt">Table of n, a(n) for n = 1..68</a>
%H A302235 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HypercubeGraph.html">Hypercube Graph</a>
%H A302235 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Matching-GeneratingPolynomial.html">Matching-Generating Polynomial</a>
%e A302235 Rows as matching-generating polynomials:
%e A302235 1 + x,
%e A302235 1 + 4*x + 2*x^2
%e A302235 1 + 12*x + 42*x^2 + 44*x^3 + 9*x^4
%e A302235 1 + 32*x + 400*x^2 + 2496*x^3 + 8256*x^4 + 14208*x^5 + 11648*x^6 + 3712*x^7 + 272*x^8
%e A302235 ...
%Y A302235 Row sums are A045310.
%Y A302235 Columns k=0..2 are A000012, A001787, A360786.
%Y A302235 Cf. A005271 (rightmost terms), A192437.
%K A302235 nonn,tabl
%O A302235 1,4
%A A302235 _Eric W. Weisstein_, Apr 03 2018