%I #15 Sep 08 2022 08:45:11
%S 2,1,5,7,21,41,107,239,593,1393,3395,8119,19665,47321,114371,275807,
%T 666113,1607521,3881411,9369319,22620561,54608393,131838371,318281039,
%U 768402497,1855077841,4478562275,10812186007,26102942481,63018038201
%N Expansion of e.g.f.: cosh(sqrt(2)*x)*(1+exp(x)).
%H G. C. Greubel, <a href="/A088014/b088014.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,-4,-2)
%F G.f.: (x-2)*(2*x-1)*(1+x) / ( (2*x^2-1)*(x^2+2*x-1) ).
%F E.g.f.: cosh(sqrt(2)*x)*(1+exp(x)).
%F a(n) = ((sqrt(2))^n + (-sqrt(2))^n + (1+sqrt(2))^n + (1-sqrt(2))^n)/2.
%F a(0)=2, a(1)=1, a(2)=5, a(3)=7, a(n) = 2*a(n-1) + 3*a(n-2) - 4*a(n-3) - 2*a(n-4). - _Harvey P. Dale_, Jul 31 2012
%t With[{nn=30},CoefficientList[Series[Cosh[Sqrt[2]x](1+Exp[x]),{x,0,nn}],x]Range[0,nn]!] (* or *) LinearRecurrence[{2,3,-4,-2},{2,1,5,7},30] (* _Harvey P. Dale_, Jul 31 2012 *)
%o (PARI) x='x+O('x^50); Vec((x-2)*(2*x-1)*(1+x)/((2*x^2-1)*(x^2+2*x-1))) \\ _G. C. Greubel_, Aug 16 2018
%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((x-2)*(2*x-1)*(1+x)/((2*x^2-1)*(x^2+2*x-1)))); // _G. C. Greubel_, Aug 16 2018
%Y Cf. A052950.
%Y Cf. A002315.
%K easy,nonn
%O 0,1
%A _Paul Barry_, Sep 18 2003