A000813 Expansion of (sin x + cos x)/cos 4x.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• R. J. Mathar, Table of n, a(n) for n = 0..200

Crossrefs

a(2n) = A001728(n). Cf. A006873, A156201, A156205.

Programs

Maple

p := proc(n) local j; 2*I*(1+add(binomial(n,j)*polylog(-j,I)*4^j, j=0..n)) end:  A000813 := n -> -(-1)^iquo(n,2)*Re(p(n));
seq(A000813(i),i=0..11);  # Peter Luschny, Apr 29 2013

Mathematica

a[n_] := 2*(-1)^Floor[n/2]*Im[Sum[4^j*Binomial[n, j]*PolyLog[-j, I], {j, 0, n}]]; Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Apr 30 2013, after Peter Luschny *)
With[{nn=20},CoefficientList[Series[(Sin[x]+Cos[x])/Cos[4x],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Dec 12 2013 *)

PARI

x='x+O('x^66); Vec(serlaplace((sin(x)+cos(x))/cos(4*x))) \\ Joerg Arndt, Apr 30 2013

Formula

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