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A000813
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Expansion of (sin x + cos x)/cos 4x.
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4
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1, 1, 15, 47, 1185, 6241, 230895, 1704527, 83860545, 796079041, 48942778575, 567864586607, 41893214676705, 574448847467041, 49441928730798255, 782259922208550287, 76946148390480577665, 1379749466246228538241
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OFFSET
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0,3
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LINKS
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FORMULA
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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
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MAPLE
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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));
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MATHEMATICA
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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 *)
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PROG
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(PARI) x='x+O('x^66); Vec(serlaplace((sin(x)+cos(x))/cos(4*x))) \\ Joerg Arndt, Apr 30 2013
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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