%I A043301
%S A043301 1,3,13,77,591,5627,64261,857901,13125559,226566107,4357258269,
%T A043301 92408688077,2142828858847,53940356223483,1464960933469429,
%U A043301 42699628495507373,1329548327094606279,44045893308104036699
%N A043301 2^n*Sum_{ k=0..n } (n+k)!/((n-k)!*k!*4^k).
%D A043301 Bruce Berndt, Ramanujan's Notebooks Part II, Springer-Verlag; see Integrals 
               and Asymptotic Expansions, p. 229.
%D A043301 I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and P 
               roducts, 6th ed., Section 3.737.1, p. 423.
%F A043301 a(n)=(2*n-1)*a(n-1)+4*a(n-2), n>1.
%F A043301 2^(n+1)n!(e^2/Pi)*Integral(t=0, infinity, cos(2t)/(1+t^2)^(n+1)dt).
%F A043301 E.g.f.: 2*(e^2/Pi)*Integral(t=0, infinity, cos(2t)/(1+t^2-2x)dt).
%F A043301 2^n * y_n(1/2), where y_n(x) are the Bessel polynomials A001498.
%Y A043301 Cf. A043302, A144505.
%Y A043301 Sequence in context: A159662 A032035 A127127 this_sequence A141762 A062872 
               A159312
%Y A043301 Adjacent sequences: A043298 A043299 A043300 this_sequence A043302 A043303 
               A043304
%K A043301 nonn,easy
%O A043301 0,2
%A A043301 Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 04 2002
%E A043301 Edited by Michael Somos, Jul 16 2002