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A088014 Expansion of e.g.f.: cosh(sqrt(2)*x)*(1+exp(x)). 3

%I

%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

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Last modified September 18 09:22 EDT 2020. Contains 337166 sequences. (Running on oeis4.)