A121376 Numerator of PolyLog[ -n, 1/n ].

-1, 6, 33, 380, 3535, 189714, 285929, 319735800, 1160703963, 145739620510, 86294277091, 10914811650686580, 60229285882649, 163637596919801624970, 3392462704290802545, 669084376596453009616, 370468452361579892135179, 157145213515550643044429571846

Offset

1,2

Comments

PolyLog[n,z] = Sum[ z^k/k^n, {k,1,Infinity} ]. PolyLog[ -n,1/n] = Sum[ k^n/n^k, {k,1,Infinity}] for n>1. n divides a(n). p^k divides a(p^k) for all prime p and integer k>0. p^k divides a(p^k-1) for prime p>2 and integer k>0.

Links

Table of n, a(n) for n=1..18.

Eric Weisstein's World of Mathematics, Polylogarithm.

Formula

a(n) = Numerator[ PolyLog[ -n, 1/n ] ]. For n>1 a(n) = Numerator[ (-1)^n * PolyLog[ -n, n ] ].

For n>1, a(n) is the numerator of n*A122778(n)/(n-1)^(n+1) = Sum[k=0..n] A(n,k)*n^(k+1)/(n-1)^(n+1). For n>1, a(n) = n * A122778(n)/gcd(A122778(n),(n-1)^(n+1)). - Max Alekseyev, Sep 11 2006

Example

PolyLog[ -n,1/n] begins -1/12, 6, 33/8, 380/81, 3535/512, 189714/15625, ...

Mathematica

Numerator[Table[PolyLog[ -n, 1/n], {n, 1, 40}]]

Prog

(PARI) a(n)=numerator(polylog(-n, 1/n)) \\ Charles R Greathouse IV, Jul 14 2014

Crossrefs

Cf. A119758.

Sequence in context: A306182 A354888 A358595 * A354890 A046707 A337825

Adjacent sequences: A121373 A121374 A121375 * A121377 A121378 A121379

Keyword

frac,sign

Author

Alexander Adamchuk, Sep 06 2006

Status

approved