A304980 a(n) = 4^n * (1 - 4^n) * Bernoulli(2*n) / (2*n) + EulerE(2*n).

-2, 7, -77, 1657, -58457, 3056557, -221729237, 21295269457, -2614745018417, 399460073350357, -74300372446261997, 16529958050063939257, -4333993989483331875977, 1322511243007573825356157, -464663077436832702395156357, 186233354336664458732835601057

Offset: 1

Author

Daniel Suteu, May 22 2018

Keywords

• sign

Crossrefs

Cf. A000367 (Bernoulli numerators), A002445 (Bernoulli denominators), A028296 (EulerE(2*n)), A241242.

Cf. A000182 (tangent numbers), A000364 (secant numbers).

Programs

Mathematica

Array[4^#*(1 - 4^#) BernoulliB[2 #]/(2 #) + EulerE[2 #] &, 16] (* Michael De Vlieger, May 24 2018 *)

PARI

a(n) = 4^n * (1 - 4^n) * bernfrac(2*n) / (2*n) + 2*imag(polylog(-2*n, I)); \\ Michel Marcus, May 30 2018

Formula

a(n) = (-1)^n * (A000182(n) + A000364(n)).