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%I #9 May 12 2022 15:19:16
%S 1,1,1,1,13,1,1,121,121,1,1,1093,4081,1093,1,1,9841,111721,111721,
%T 9841,1,1,88573,2880481,7256173,2880481,88573,1,1,797161,72799321,
%U 403087441,403087441,72799321,797161,1,1,7174453,1827068881,20966597653,42931692481,20966597653,1827068881,7174453,1
%N Array T(n,k) = D(2*n, -2*k-1), where D(i,j) are the polysecant numbers, for n,k >= 0, read by antidiagonals.
%H Masanobu Kaneko, Maneka Pallewatta, and Hirofumi Tsumura, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL23/Tsumura/tsumura3.html">On Polycosecant Numbers</a>, J. Integer Seq. 23 (2020), no. 6, 17 pp. See Table 2 p. 9.
%H Kyosuke Nishibiro, <a href="https://arxiv.org/abs/2205.05247">On some properties of polycosecant numbers and polycotangent numbers</a>, arXiv:2205.05247 [math.NT], 2022.
%F D(n, k) = Sum_{m=0..floor(n/2)} (1/(2*m+1)^(k+1))*Sum_{p=2*m..n} (-1)^p*(p+1)!*binomial(p, 2*m)*Stirling2(n+1,p+1)/2^p)).
%e The array begins:
%e 1 1 1 1 1 ...
%e 1 13 121 1093 9841 ...
%e 1 121 4081 111721 2880481 ...
%e 1 1093 111721 7256173 403087441 ...
%e 1 9841 2880481 403087441 42931692481 ...
%e ...
%o (PARI) D(n, k) = sum(m=0, n\2, (1/(2*m+1)^(k+1))*sum(p=2*m, n, (-1)^p*(p+1)!*binomial(p, 2*m)*stirling(n+1,p+1,2)/2^p));
%o matrix(5,5,n, k, n--; k--; D(2*n,-2*k-1))
%Y Cf. A008277 (Stirling2), A001896, A001897, A353953.
%K nonn,tabl
%O 0,5
%A _Michel Marcus_, May 12 2022
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