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

1, 1, 1, 4, 2, 1, 12, 42, 44, 9, 1, 32, 400, 2496, 8256, 14208, 11648, 3712, 272, 1, 80, 2840, 59120, 803580, 7517264, 49715240, 235146480, 795862790, 1910146160, 3190117800, 3594554960, 2605908220, 1129177840, 259084440, 25108944, 589185, 1, 192, 17376, 986240

Offset: 1

Author

Eric W. Weisstein, Apr 03 2018

Keywords

• nonn
• tabl

Examples

			Rows as matching-generating polynomials:
1 + x,
1 + 4*x + 2*x^2
1 + 12*x + 42*x^2 + 44*x^3 + 9*x^4
1 + 32*x + 400*x^2 + 2496*x^3 + 8256*x^4 + 14208*x^5 + 11648*x^6 + 3712*x^7 + 272*x^8
...
		

Links

• Eric W. Weisstein, Table of n, a(n) for n = 1..68
• Eric Weisstein's World of Mathematics, Hypercube Graph
• Eric Weisstein's World of Mathematics, Matching-Generating Polynomial

Crossrefs

Row sums are A045310.

Columns k=0..2 are A000012, A001787, A360786.

Cf. A005271 (rightmost terms), A192437.