cp's OEIS Frontend

A029582 E.g.f. sin(x) + cos(x) + tan(x).

%I A029582 #20 Jul 08 2025 19:14:41
%S A029582 1,2,-1,1,1,17,-1,271,1,7937,-1,353791,1,22368257,-1,1903757311,1,
%T A029582 209865342977,-1,29088885112831,1,4951498053124097,-1,
%U A029582 1015423886506852351,1,246921480190207983617,-1,70251601603943959887871,1,23119184187809597841473537
%N A029582 E.g.f. sin(x) + cos(x) + tan(x).
%H A029582 T. D. Noe, <a href="/A029582/b029582.txt">Table of n, a(n) for n = 0..100</a>
%F A029582 G.f.: (1+x)/(1+x^2)+x/T(0) where T(k)=  1 - (k+1)*(k+2)*x^2/T(k+1) ; (recursively defined continued fraction). - _Sergei N. Gladkovskii_, Feb 12 2013
%F A029582 G.f.: (1+x)/(1+x^2)+x/G(0) where G(k) = 1 - 2*x^2*(4*k^2+4*k+1) - 4*x^4*(k+1)^2*(4*k^2+8*k+3)/G(k+1); (recursively defined continued fraction). - _Sergei N. Gladkovskii_, Feb 12 2013
%t A029582 nn = 30; Range[0, nn]! CoefficientList[Series[Tan[x] + Sin[x] + Cos[x], {x, 0, nn}], x] (* _T. D. Noe_, Jul 16 2012 *)
%o A029582 (Sage) # Variant of an algorithm of L. Seidel (1877).
%o A029582 def A029582_list(n) :
%o A029582     dim = 2*n; E = matrix(ZZ, dim); E[0, 0] = 1
%o A029582     for m in (1..dim-1) :
%o A029582         if m % 2 == 0 :
%o A029582             E[m, 0] = 1;
%o A029582             for k in range(m-1, -1, -1) :
%o A029582                 E[k, m-k] = E[k+1, m-k-1] - E[k, m-k-1]
%o A029582         else :
%o A029582             E[0, m] = 1;
%o A029582             for k in range(1, m+1, 1) :
%o A029582                 E[k, m-k] = E[k-1, m-k+1] + E[k-1, m-k]
%o A029582     return [(-1)^(k//2)*E[k,0] for k in range(dim)]
%o A029582 A029582_list(15)  # _Peter Luschny_, Jul 14 2012
%Y A029582 Cf. A009744, A099023.
%K A029582 sign
%O A029582 0,2
%A A029582 _N. J. A. Sloane_