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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
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.
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: A197230 A025171 A375885 * A127214 A304194 A124723
KEYWORD
nonn,frac
AUTHOR
Peter Luschny, Mar 22 2021
STATUS
approved