A156205 Numerator of Euler(n, 3/8).

1, -1, -15, 47, 1185, -6241, -230895, 1704527, 83860545, -796079041, -48942778575, 567864586607, 41893214676705, -574448847467041, -49441928730798255, 782259922208550287, 76946148390480577665, -1379749466246228538241, -152682246738275154625935

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

a(n) = (-1)^(n+1)*Re(2*I*(1+sum_{j=0..n}(binomial(n,j)*Li_{-j}(I)*4^j))). - Peter Luschny, Apr 29 2013

a(n) = (-4)^n*skp(n, 1/4), where skp(n,x) are the Swiss-Knife polynomials A153641. - Peter Luschny, Apr 19 2014

Maple

p := proc(n) local j; 2*I*(1+add(binomial(n, j)*polylog(-j, I)*4^j, j=0..n)) end:  A156205 := n -> (-1)^(n+1)*Re(p(n));
seq(A156205(i), i=0..11);  # Peter Luschny, Apr 29 2013

Mathematica

Numerator[EulerE[Range[0, 20], 3/8]] (* Vincenzo Librandi, May 04 2012 *)

Crossrefs

For denominators see A001018. Cf. A000813.

Sequence in context: A063396 A236401 A000813 * A065906 A370912 A377521

Adjacent sequences: A156202 A156203 A156204 * A156206 A156207 A156208

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 07 2009

Status

approved