A342319 a(n) = denominator(((i^n * PolyLog(1 - n, -i) + (-i)^n * PolyLog(1 - n, i))) / (4^n - 2^n)) if n > 0 and a(0) = 1. Here i denotes the imaginary unit.

1, 2, 12, 56, 120, 992, 252, 16256, 240, 261632, 132, 4192256, 32760, 67100672, 12, 1073709056, 8160, 17179738112, 14364, 274877382656, 6600, 4398044413952, 276, 70368735789056, 65520, 1125899873288192, 12, 18014398375264256, 3480, 288230375614840832

Offset

0,2

Comments

For comments and references see A342318.

Links

Table of n, a(n) for n=0..29.

Formula

a(2*n) = A006953(n).

a(2*n+1) = A193475(n).

Example

r(n) = 1, 1/2, 1/12, 1/56, 1/120, 5/992, 1/252, 61/16256, 1/240, 1385/261632, 1/132, ...

Maple

a := n -> `if`(n = 0, 1, `if`(n::even, denom(abs(bernoulli(n))/n), 4^n - 2^n)):
seq(a(n), n=0..29);

Mathematica

r[s_] := If[s == 0, 1, (I^s PolyLog[1 - s, -I] + (-I)^s PolyLog[1 - s, I]) / (4^s - 2^s)]; Table[r[n], {n, 0, 29}] // Denominator

Crossrefs

Cf. A342318 (numerator), A006953, A193475.

Sequence in context: A181541 A197230 A025171 * A127214 A304194 A124723

Adjacent sequences: A342316 A342317 A342318 * A342320 A342321 A342322

Keyword

nonn,frac

Author

Peter Luschny, Mar 22 2021

Status

approved