A143197 Triangle read by rows: imaginary part of polylog expansion of Eulerian numbers: p(x,n) = (1 - I*x)^(n + 1)*PolyLog(-n, I*x)/x.

1, 1, 1, 0, 1, 0, -1, 1, 0, -11, 0, 1, 0, -66, 0, 1, 1, 0, -302, 0, 57, 0, 1, 0, -1191, 0, 1191, 0, -1, 1, 0, -4293, 0, 15619, 0, -247, 0, 1, 0, -14608, 0, 156190, 0, -14608, 0, 1, 1, 0, -47840, 0, 1310354, 0, -455192, 0, 1013, 0

Offset

1,10

Links

Table of n, a(n) for n=1..56.

Formula

p(x,n) = (1 - I*x)^(n + 1)*PolyLog(-n, I*x)/x;

t(n,m) = ImaginaryCoefficients(p(x,n)).

Example

Triangle begins
  1;
  1;
  1, 0;
  1, 0,     -1;
  1, 0,    -11, 0;
  1, 0,    -66, 0,       1;
  1, 0,   -302, 0,      57, 0;
  1, 0,  -1191, 0,    1191, 0,      -1;
  1, 0,  -4293, 0,   15619, 0,    -247, 0;
  1, 0, -14608, 0,  156190, 0,  -14608, 0,    1;
  1, 0, -47840, 0, 1310354, 0, -455192, 0, 1013, 0;

Mathematica

p[x_, n_] = p[x_, n_] = (1 - I*x)^(n + 1)*PolyLog[ -n, I*x]/x;
Table[FullSimplify[Expand[p[x, n]]], {n, 0, 10}];
Table[Im[CoefficientList[FullSimplify[Expand[p[x, n]]], x]], {n, 0, 10}];
Flatten[%]

Crossrefs

Cf. A060187.

Sequence in context: A179920 A216726 A323169 * A138066 A173189 A115595

Adjacent sequences: A143194 A143195 A143196 * A143198 A143199 A143200

Keyword

tabf,uned,sign,less

Author

Roger L. Bagula, Oct 19 2008

Extensions

The entries here are clearly all wrong (compare the example lines). What are the real parts? - N. J. A. Sloane, Oct 25 2008

The entries were those of A143196; entries replaced with those in the example by Georg Fischer, Nov 03 2018

Status

approved