OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
a(n) = Im(2*((1-I)/(1+I))^n*(1+sum_{j=0..n}(binomial(n,j)*Li_{-j}(I)* 4^j))). - Peter Luschny, Apr 29 2013
a(n) ~ n! * sqrt(2+sqrt(2)) * 2^(3*n+1)/Pi^(n+1). - Vaclav Kotesovec, Jun 02 2013
MAPLE
per4 := proc(n) local j; 2*((1-I)/(1+I))^n*(1+add(binomial(n, j)* polylog(-j, I)*4^j, j=0..n)) end: A225109 := n -> Im(per4(n));
seq(A225109(i), i=0..11); # Peter Luschny, Apr 29 2013
MATHEMATICA
mx = 17; Range[0, mx]! CoefficientList[ Series[ (Sin[3x] + Cos[x])/Cos[4x], {x, 0, mx}], x] (* Robert G. Wilson v, Apr 28 2013 *)
PROG
(PARI) v=Vec((sin(3*x) + cos(x)) / cos(4*x)); vector(#v, i, v[i]*(i-1)!)
(PARI) x='x+O('x^66); Vec(serlaplace((sin(3*x)+cos(x))/cos(4*x))) \\ Joerg Arndt, Apr 28 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
M. F. Hasler, Apr 28 2013
STATUS
approved