cp's OEIS Frontend

A373660 Triangle read by rows: T(n, k) = (-1)^k*binomial(n, k) * A050446(n, n - k).

%I A373660 #9 Jun 13 2024 02:04:05
%S A373660 1,2,-1,6,-6,1,30,-42,15,-1,190,-340,186,-32,1,1547,-3355,2460,-700,
%T A373660 65,-1,15106,-38430,35295,-14140,2355,-126,1,173502,-506114,558285,
%U A373660 -289520,71295,-7413,238,-1,2286648,-7520040,9681700,-6174224,2033920,-328384,22204,-440,1
%N A373660 Triangle read by rows: T(n, k) = (-1)^k*binomial(n, k) * A050446(n, n - k).
%H A373660 Guoce Xin and Yueming Zhong, <a href="https://arxiv.org/abs/2201.02376">Proving some conjectures on Kekulé numbers for certain benzenoids by using Chebyshev polynomials</a>, arXiv:2201.02376 [math.CO], 2022.
%F A373660 Row sums are the Euler numbers A000111.
%e A373660 Triangle starts:
%e A373660   [0]      1;
%e A373660   [1]      2,      -1;
%e A373660   [2]      6,      -6,      1;
%e A373660   [3]     30,     -42,     15,      -1;
%e A373660   [4]    190,    -340,    186,     -32,     1;
%e A373660   [5]   1547,   -3355,   2460,    -700,    65,    -1;
%e A373660   [6]  15106,  -38430,  35295,  -14140,  2355,  -126,   1;
%e A373660   [7] 173502, -506114, 558285, -289520, 71295, -7413, 238, -1;
%p A373660 T := (n, k) -> (-1)^k*binomial(n, k) * A050446(n, n - k):
%p A373660 for n from 0 to 7 do print(seq(T(n, k), k=0..n)) od;
%Y A373660 Cf. A050446, A373659 (column 0), A000111 (row sums), A373658 (alternating row sums).
%K A373660 sign,tabl
%O A373660 0,2
%A A373660 _Peter Luschny_, Jun 12 2024