cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

Original entry on oeis.org

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

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Author

Peter Luschny, Mar 22 2021

Keywords

Comments

For comments and references see A342318.

Examples

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

Crossrefs

Cf. A342318 (numerator), A006953, A193475.

Programs

  • 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

Formula

a(2*n) = A006953(n).
a(2*n+1) = A193475(n).