A374621 Expansion of e.g.f. 1 - x^4/24 - log(1 - x).

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)

Links

Table of n, a(n) for n=0..24.

Wikipedia, Toeplitz Matrix.

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

Cf. A369833.

Cf. A374617, A374618, A374619, A374620.

Sequence in context: A284230 A374926 A364229 * A052111 A176473 A185056

Adjacent sequences: A374618 A374619 A374620 * A374622 A374623 A374624

Keyword

nonn,easy

Author

Stefano Spezia, Jul 14 2024

Status

approved