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%I #14 Sep 08 2022 08:45:10
%S 1,6,36,218,1336,8280,51776,325792,2057856,13023104,82456576,
%T 521826816,3298727936,20822038528,131210919936,825373859840,
%U 5182772248576,32487861092352,203308891897856,1270289732337664,7924975155019776
%N Expansion of e.g.f.: (1+x)*exp(5*x)*cosh(x).
%C Binomial transform of A082307.
%H G. C. Greubel, <a href="/A082309/b082309.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 (20,-148,480,-576).
%F a(n) = (A081106(n) + A079028(n))/2.
%F a(n) = ((n+4)*4^(n-1) + (n+6)*6^(n-1))/2.
%F G.f.: ((1-5*x)/(1-6*x)^2 + (1-3*x)/(1-4*x)^2)/2.
%F From _Harvey P. Dale_, Aug 27 2012: (Start)
%F E.g.f.: (1+x)*exp(5*x)*cosh(x).
%F a(n) = 20*a(n-1) - 148*a(n-2) + 480*a(n-3) - 576*a(n-4), n>3. (End)
%t With[{nn=30},CoefficientList[Series[(1+x)Exp[5x]Cosh[x],{x,0,nn}],x]Range[0,nn]!] (* or *) LinearRecurrence[{20,-148,480,-576},{1,6,36,218},30] (* _Harvey P. Dale_, Aug 27 2012 *)
%o (PARI) x='x+O('x^30); Vec(serlaplace((1+x)*exp(5*x)*cosh(x))) \\ _G. C. Greubel_, Sep 16 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!((1+x)*Exp(5*x)*Cosh(x))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Sep 16 2018
%Y Cf. A082308, A082307, A082306, A082305.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Apr 09 2003
%E Definition clarified by _Harvey P. Dale_, Aug 27 2012
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