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

Author

N. J. A. Sloane, Nov 07 2009

Keywords

• sign
• frac

Links

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

Crossrefs

For denominators see A001018. Cf. A000813.

Programs

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 *)

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