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

%I #25 Dec 30 2017 14:32:21

%S 1,1,15,47,1185,6241,230895,1704527,83860545,796079041,48942778575,

%T 567864586607,41893214676705,574448847467041,49441928730798255,

%U 782259922208550287,76946148390480577665,1379749466246228538241

%N Expansion of (sin x + cos x)/cos 4x.

%H R. J. Mathar, <a href="/A000813/b000813.txt">Table of n, a(n) for n = 0..200</a>

%F 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

%p 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));

%p seq(A000813(i),i=0..11); # _Peter Luschny_, Apr 29 2013

%t 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_ *)

%t With[{nn=20},CoefficientList[Series[(Sin[x]+Cos[x])/Cos[4x],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Dec 12 2013 *)

%o (PARI) x='x+O('x^66); Vec(serlaplace((sin(x)+cos(x))/cos(4*x))) \\ _Joerg Arndt_, Apr 30 2013

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

%K nonn

%O 0,3

%A _N. J. A. Sloane_

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Last modified March 28 10:31 EDT 2024. Contains 371240 sequences. (Running on oeis4.)