The OEIS is supported by the many generous donors to the OEIS Foundation.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #5 May 12 2022 15:19:10
%S 1,1,1,1,2,1,1,8,5,1,1,32,41,14,1,1,128,365,200,41,1,1,512,3281,3104,
%T 977,122,1,1,2048,29525,49280,23801,4808,365,1,1,8192,265721,786944,
%U 589217,174752,23801,1094,1,1,32768,2391485,12584960,14677961,6297728,1257125,118280,3281,1
%N Array T(n,k) = beta(2*n, -k), where beta(i,j) are the polycotangent numbers, for n,k >= 0, read by ascending 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.
%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.
%e The array begins:
%e 1 1 1 1 1 ...
%e 1 2 5 14 41 ...
%e 1 8 41 200 977 ...
%e 1 32 365 3104 23801 ...
%e 1 128 3281 49280 589217 ...
%o (PARI) beta(n,k) = if (!(n%2), n>>=1; sum(j=0, 2*n, sum(i=0, j\2, (-1)^j*j!*binomial(j+1,2*i+1)*((j+1)*(j+2)*stirling(2*n,j+2,2)/2+stirling(2*n+1,j+1,2))/(2^j*(2*i+1)^k))));
%o matrix(5,5,n, k, n--; k--; beta(2*n,-k))
%K nonn,tabl
%O 0,5
%A _Michel Marcus_, May 12 2022