A346720 a(n) is the number of negative Euler permutations of order 2*n. Bisection (even indices) of A347602.

0, 1, 2, 163, 6724, 692741, 86756038, 16135231015, 3838836369800, 1178853270354697, 447322130002332298, 206783054242756958891, 114117348385587556703692, 74183362210489714472590093, 56080450787901009525514063694, 48790757690364513377740990959151, 48400123863374755985614486072403728

Offset: 0

Author

Peter Luschny, Sep 09 2021

Keywords

• nonn

Comments

For definitions and comments see A347602.

Crossrefs

Cf. A347601, A346719, A000166, A000364, A347602.

Programs

Maple

# uses A000166.
A346720 := n -> (A000166(2*n) - euler(2*n)) / 2:
seq(A346720(n), n = 0..16);

Mathematica

A346720[n_] := Subfactorial[2 n]/2 - Im[PolyLog[-2 n, I]];
Table[A346720[n], {n, 0, 16}]

Formula

A346719(n) + a(n) = A000166(2n) (rencontres numbers).

A346719(n) - a(n) = A000364(n) (Euler secant numbers).

a(n) = subfactorial(2*n) / 2 - Im(PolyLog(-2*n, i)).