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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 16 02:16 EDT 2019. Contains 327088 sequences. (Running on oeis4.)