A362308 Triangle read by rows. Number of perfect matchings by number of connected components.
1, 0, 1, 0, 2, 1, 0, 10, 4, 1, 0, 74, 24, 6, 1, 0, 706, 188, 42, 8, 1, 0, 8162, 1808, 350, 64, 10, 1, 0, 110410, 20628, 3426, 568, 90, 12, 1, 0, 1708394, 273064, 38886, 5696, 850, 120, 14, 1
Offset: 0
Examples
Table T(n, k) begins: [0] 1; [1] 0, 1; [2] 0, 2, 1; [3] 0, 10, 4, 1; [4] 0, 74, 24, 6, 1; [5] 0, 706, 188, 42, 8, 1; [6] 0, 8162, 1808, 350, 64, 10, 1; [7] 0, 110410, 20628, 3426, 568, 90, 12, 1; [8] 0, 1708394, 273064, 38886, 5696, 850, 120, 14, 1;
Links
- Alan D. Sokal and Jiang Zeng, Some multivariate master polynomials for permutations, set partitions, and perfect matchings, and their continued fractions, Advances in Applied Mathematics, Volume 138, 2022. Table on p. 91.
- Wikipedia, Perfect matching.
Crossrefs
Formula
T(n, k) = T(n, k-1) - T(n-1, k-2) - (2*n - k - 1)/(k - 1) * T(n - 1, k - 1) for k > 1. - Detlef Meya, Dec 21 2023
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