A373660 Triangle read by rows: T(n, k) = (-1)^k*binomial(n, k) * A050446(n, n - k).
1, 2, -1, 6, -6, 1, 30, -42, 15, -1, 190, -340, 186, -32, 1, 1547, -3355, 2460, -700, 65, -1, 15106, -38430, 35295, -14140, 2355, -126, 1, 173502, -506114, 558285, -289520, 71295, -7413, 238, -1, 2286648, -7520040, 9681700, -6174224, 2033920, -328384, 22204, -440, 1
Offset: 0
Examples
Triangle starts: [0] 1; [1] 2, -1; [2] 6, -6, 1; [3] 30, -42, 15, -1; [4] 190, -340, 186, -32, 1; [5] 1547, -3355, 2460, -700, 65, -1; [6] 15106, -38430, 35295, -14140, 2355, -126, 1; [7] 173502, -506114, 558285, -289520, 71295, -7413, 238, -1;
Links
- Guoce Xin and Yueming Zhong, Proving some conjectures on Kekulé numbers for certain benzenoids by using Chebyshev polynomials, arXiv:2201.02376 [math.CO], 2022.
Programs
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Maple
T := (n, k) -> (-1)^k*binomial(n, k) * A050446(n, n - k): for n from 0 to 7 do print(seq(T(n, k), k=0..n)) od;
Formula
Row sums are the Euler numbers A000111.