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A292792 The imaginary part of E(2n, i)/i, where E(n, x) is the Euler polynomial.

%I A292792 #24 Oct 22 2017 07:46:26
%S A292792 -1,3,-11,63,-571,7623,-140531,3417183,-105946891,4079170743,
%T A292792 -190947551651,10679561580303,-703342782666811,53875223570677863,
%U A292792 -4749070236390684371,477331966210918815423,-54264228263241408276331,6927625954707653092264983,-986892857756676619338994691
%N A292792 The imaginary part of E(2n, i)/i, where E(n, x) is the Euler polynomial.
%C A292792 The real part is +- 1.
%C A292792 For E(2n-1, i) see A292791.
%C A292792 a(2n) == 3 (mod 6),
%C A292792 a(4n+1) == 5 (mod 6),
%C A292792 a(4n+3) == 1 (mod 6).
%C A292792 Inspired by A291897.
%C A292792 Also the negative imaginary part of E(2n, 1+i) or the imaginary part of E(2n, 1-i).
%H A292792 Robert G. Wilson v, <a href="/A292792/b292792.txt">Table of n, a(n) for n = 1..276</a>
%e A292792 a(3) = -11 since E(6, i) = -1 - 11i.
%t A292792 f[n_] := (EulerE[2n, I] - I^(2n))/I; Array[f, 19]
%Y A292792 Cf. A291897, A292791.
%K A292792 sign
%O A292792 1,2
%A A292792 _Robert G. Wilson v_, Sep 23 2017