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A000813 Expansion of (sin x + cos x)/cos 4x. 4
1, 1, 15, 47, 1185, 6241, 230895, 1704527, 83860545, 796079041, 48942778575, 567864586607, 41893214676705, 574448847467041, 49441928730798255, 782259922208550287, 76946148390480577665, 1379749466246228538241 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

R. J. Mathar, Table of n, a(n) for n = 1..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-Fran├žois 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 A154060

Adjacent sequences:  A000810 A000811 A000812 * A000814 A000815 A000816

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified June 28 14:30 EDT 2017. Contains 288838 sequences.