OFFSET
0,4
COMMENTS
This sequence is an extension of the even-indexed Euler numbers A028296. These numbers can be extended to A000111 by adding the expansion of the tangent function, respectively considering the alternating permutations. Here one gets a different extension of the nonzero Euler numbers by considering the permutations A347601 and A347602 based on the permanent of the tangent matrix as defined in A346831. An overview gives a table in A347601.
MAPLE
PROG
(Sage)
def TangentMatrix(N):
M = matrix(N, N)
H = (N + 1) // 2
for n in range(1, N):
for k in range(n):
M[n - k - 1, k] = 1 if n < H else -1
M[N - n + k, N - k - 1] = -1 if n < N - H else 1
return M
def A347598(n):
if n == 0: return 1
return TangentMatrix(n).permanent()
print([A347598(n) for n in range(12)])
CROSSREFS
KEYWORD
sign
AUTHOR
Peter Luschny, Sep 12 2021
STATUS
approved