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

0,3

Links

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

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A166118 A063396 A236401 * A156205 A065906 A370912

Adjacent sequences: A000810 A000811 A000812 * A000814 A000815 A000816

Keyword

nonn

Author

N. J. A. Sloane

Status

approved