A395339 - OEIS

%I #11 Apr 20 2026 09:22:34

%S 1,-1,-3,59,-263,119,5877,-38221,82417,461039,-4826643,17433899,

%T 16062697,-532223641,2791774437,-3445055581,-49124027423,380870554079,

%U -1057122638883,-3179028018661,45502234084057,-193537704037801,23670372125397,4696420368192659,-28770281512290863

%N a(n) = (2*n)! * [x^(2*n)] cosh(x) * cos(x)^2.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-5,-19,25).

%F a(n) = (Re((1+2*i)^(2*n)) + 1)/2, where i = sqrt(-1).

%F G.f.: (1+4*x+11*x^2)/((1-x) * (1+6*x+25*x^2)).

%F a(n) = -5*a(n-1) - 19*a(n-2) + 25*a(n-3).

%o (PARI) a(n) = (real((1+2*I)^(2*n))+1)/2;

%Y Cf. A066771, A199572, A395340.

%K sign,easy

%O 0,3

%A _Seiichi Manyama_, Apr 20 2026