OFFSET
0,5
LINKS
Masanobu Kaneko, Maneka Pallewatta, and Hirofumi Tsumura, On Polycosecant Numbers, J. Integer Seq. 23 (2020), no. 6, 17 pp.
Kyosuke Nishibiro, On some properties of polycosecant numbers and polycotangent numbers, arXiv:2205.05247 [math.NT], 2022.
EXAMPLE
The array begins:
1 1 1 1 1 ...
1 2 5 14 41 ...
1 8 41 200 977 ...
1 32 365 3104 23801 ...
1 128 3281 49280 589217 ...
PROG
(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))));
matrix(5, 5, n, k, n--; k--; beta(2*n, -k))
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Michel Marcus, May 12 2022
STATUS
approved