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%I #9 Sep 16 2021 03:47:21
%S 0,1,2,163,6724,692741,86756038,16135231015,3838836369800,
%T 1178853270354697,447322130002332298,206783054242756958891,
%U 114117348385587556703692,74183362210489714472590093,56080450787901009525514063694,48790757690364513377740990959151,48400123863374755985614486072403728
%N a(n) is the number of negative Euler permutations of order 2*n. Bisection (even indices) of A347602.
%C For definitions and comments see A347602.
%F A346719(n) + a(n) = A000166(2n) (rencontres numbers).
%F A346719(n) - a(n) = A000364(n) (Euler secant numbers).
%F a(n) = subfactorial(2*n) / 2 - Im(PolyLog(-2*n, i)).
%p # uses A000166.
%p A346720 := n -> (A000166(2*n) - euler(2*n)) / 2:
%p seq(A346720(n), n = 0..16);
%t A346720[n_] := Subfactorial[2 n]/2 - Im[PolyLog[-2 n, I]];
%t Table[A346720[n], {n, 0, 16}]
%Y Cf. A347601, A346719, A000166, A000364, A347602.
%K nonn
%O 0,3
%A _Peter Luschny_, Sep 09 2021
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