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%I #13 Jun 25 2018 03:52:06
%S -2,7,-77,1657,-58457,3056557,-221729237,21295269457,-2614745018417,
%T 399460073350357,-74300372446261997,16529958050063939257,
%U -4333993989483331875977,1322511243007573825356157,-464663077436832702395156357,186233354336664458732835601057
%N a(n) = 4^n * (1 - 4^n) * Bernoulli(2*n) / (2*n) + EulerE(2*n).
%F a(n) = (-1)^n * (A000182(n) + A000364(n)).
%t Array[4^#*(1 - 4^#) BernoulliB[2 #]/(2 #) + EulerE[2 #] &, 16] (* _Michael De Vlieger_, May 24 2018 *)
%o (PARI) a(n) = 4^n * (1 - 4^n) * bernfrac(2*n) / (2*n) + 2*imag(polylog(-2*n, I)); \\ _Michel Marcus_, May 30 2018
%Y Cf. A000367 (Bernoulli numerators), A002445 (Bernoulli denominators), A028296 (EulerE(2*n)), A241242.
%Y Cf. A000182 (tangent numbers), A000364 (secant numbers).
%K sign
%O 1,1
%A _Daniel Suteu_, May 22 2018