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A374621
Expansion of e.g.f. 1 - x^4/24 - log(1 - x).
4
1, 1, 1, 2, 5, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000, 121645100408832000, 2432902008176640000, 51090942171709440000, 1124000727777607680000, 25852016738884976640000
OFFSET
0,4
COMMENTS
Conjectures (confirmed up to n = 10): (Start)
a(n) is the number of distinct values of the permanent of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the integers 1, 2, ..., n-1 off-diagonal.
a(n) is the number of distinct values of the permanent of an n X n symmetric Toeplitz matrix having 0 on the main diagonal and all the first n-1 primes off-diagonal. (End)
FORMULA
a(0) = 1, a(4) = 5, and a(n) = (n-1)! for n > 0 and n <> 4.
a(n) = (n - 1)*a(n-1) for n > 5.
MATHEMATICA
nmax=24; CoefficientList[Series[1-x^4/24-Log[1-x], {x, 0, nmax}], x]*Range[0, nmax]!
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Stefano Spezia, Jul 14 2024
STATUS
approved