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A347598 a(n) = permanent(T(n)), where T(n) is the tangent matrix defined in A346831 and n >= 1; by convention a(0) = 1. 4
1, 0, -1, 2, 5, -12, -61, 230, 1385, -6936, -50521, 316682, 2702765, -20359332, -199360981, 1754340590, 19391512145, -195242324016, -2404879675441, 27266796955922, 370371188237525, -4669829301365052, -69348874393137901, 962523286888757750, 15514534163557086905 (list; graph; refs; listen; history; text; internal format)
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.
LINKS
FORMULA
a(2*n) = A028296(n); a(2*n + 1) = A347597(n).
MAPLE
# Uses the function TangentMatrix from A346831.
A347598 := n -> `if`(n = 0, 1, LinearAlgebra:-Permanent(TangentMatrix(n))):
seq(A347598(n), n = 0..12);
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
Sequence in context: A083699 A064636 A355991 * A293023 A145857 A264863
KEYWORD
sign
AUTHOR
Peter Luschny, Sep 12 2021
STATUS
approved

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Last modified June 25 02:21 EDT 2024. Contains 373691 sequences. (Running on oeis4.)