|
%I #20 Jul 17 2013 16:45:54
%S 1,3,15,117,1185,15123,230895,4116837,83860545,1921996323,48942778575,
%T 1370953667157,41893214676705,1386843017916723,49441928730798255,
%U 1888542637550347077,76946148390480577665,3331009898404800736323,152682246738275154625935,7387240827905368219116597
%N E.g.f. (sin(3x) + cos x) / cos(4x).
%H Vincenzo Librandi, <a href="/A225109/b225109.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = Im(2*((1-I)/(1+I))^n*(1+sum_{j=0..n}(binomial(n,j)*Li_{-j}(I)* 4^j))). - _Peter Luschny_, Apr 29 2013
%F a(n) ~ n! * sqrt(2+sqrt(2)) * 2^(3*n+1)/Pi^(n+1). - _Vaclav Kotesovec_, Jun 02 2013
%p per4 := proc(n) local j; 2*((1-I)/(1+I))^n*(1+add(binomial(n,j)* polylog(-j,I)*4^j, j=0..n)) end: A225109 := n -> Im(per4(n));
%p seq(A225109(i), i=0..11); # _Peter Luschny_, Apr 29 2013
%t mx = 17; Range[0, mx]! CoefficientList[ Series[ (Sin[3x] + Cos[x])/Cos[4x], {x, 0, mx}], x] (* _Robert G. Wilson v_, Apr 28 2013 *)
%o (PARI) v=Vec((sin(3*x) + cos(x)) / cos(4*x)); vector(#v,i,v[i]*(i-1)!)
%o (PARI) x='x+O('x^66); Vec(serlaplace((sin(3*x)+cos(x))/cos(4*x))) \\ _Joerg Arndt_, Apr 28 2013
%Y Cf. A006873, A007289, A007286.
%K nonn
%O 0,2
%A _M. F. Hasler_, Apr 28 2013
|
