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A156201 Numerator of Euler(n, 1/8). 2
1, -3, -7, 117, 497, -15123, -95767, 4116837, 34741217, -1921996323, -20273087527, 1370953667157, 17352768515537, -1386843017916723, -20479521468959287, 1888542637550347077, 31872138933891307457, -3331009898404800736323, -63243057486503656319047 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

T. D. Noe, Table of n, a(n) for n = 0..100

FORMULA

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

G.f.: conjecture T(0)/(1+3*x), where T(k) = 1 - 16*x^2*(k+1)^2/(16*x^2*(k+1)^2 + (1+3*x)^2/T(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Nov 12 2013

a(n) = (-4)^n*skp(n, 3/4), where skp(n,x) are the Swiss-Knife polynomials A153641. - Peter Luschny, Apr 19 2014

a(n) = 2^(4*n+1)*(zeta(-n,1/16)-zeta(-n, 9/16)), where zeta(a, z) is the generalized Riemann zeta function. - Peter Luschny, Mar 11 2015

MAPLE

p := proc(n) local j; 2*I*(1+add(binomial(n, j)*polylog(-j, I)*4^j, j=0..n)) end:  A156201 := n -> Im(p(n));

seq(A156201(i), i=0..10);  # Peter Luschny, Apr 29 2013

MATHEMATICA

Table[EulerE[n, 1/8] // Numerator, {n, 0, 18}] (* Jean-Fran├žois Alcover, Apr 30 2013 *)

CROSSREFS

For denominators see A001018. Cf. A000813.

Sequence in context: A014014 A015884 A224936 * A066771 A139159 A042329

Adjacent sequences:  A156198 A156199 A156200 * A156202 A156203 A156204

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 07 2009

STATUS

approved

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Last modified August 21 02:25 EDT 2017. Contains 290855 sequences.