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

-1, 3, -11, 63, -571, 7623, -140531, 3417183, -105946891, 4079170743, -190947551651, 10679561580303, -703342782666811, 53875223570677863, -4749070236390684371, 477331966210918815423, -54264228263241408276331, 6927625954707653092264983, -986892857756676619338994691

Offset: 1

Author

Robert G. Wilson v, Sep 23 2017

Keywords

• sign

Comments

The real part is +- 1.

For E(2n-1, i) see A292791.

a(2n) == 3 (mod 6),

a(4n+1) == 5 (mod 6),

a(4n+3) == 1 (mod 6).

Inspired by A291897.

Also the negative imaginary part of E(2n, 1+i) or the imaginary part of E(2n, 1-i).

Examples

			a(3) = -11 since E(6, i) = -1 - 11i.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..276

Crossrefs

Cf. A291897, A292791.

Programs

Mathematica

f[n_] := (EulerE[2n, I] - I^(2n))/I; Array[f, 19]