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A082308 Expansion of e.g.f. (1+x)*exp(4*x)*cosh(x).

%I A082308 #10 Sep 08 2022 08:45:10
%S A082308 1,5,25,127,657,3449,18281,97395,519841,2773741,14776377,78538343,
%T A082308 416367665,2201517153,11610231433,61078202971,320570884929,
%U A082308 1678897264085,8775159682649,45780628812879,238431945108433
%N A082308 Expansion of e.g.f. (1+x)*exp(4*x)*cosh(x).
%C A082308 Binomial transform of A082307.
%H A082308 G. C. Greubel, <a href="/A082308/b082308.txt">Table of n, a(n) for n = 0..1000</a>
%H A082308 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (16,-94,240,-225).
%F A082308 a(n) = (A081105(n) + A006234(n))/2.
%F A082308 a(n) = ((n+3)*3^(n-1) + (n+5)*5^(n-1))/2.
%F A082308 G.f.: ((1-4*x)/(1-5*x)^2 + (1-2*x)/(1-3*x)^2)/2.
%F A082308 E.g.f.: (1+x)*exp(4*x)*cosh(x) = (1+x)*(exp(5*x) + exp(3*x))/2.
%t A082308 With[{nmax = 50}, CoefficientList[Series[(1 + x)*Exp[4*x]*Cosh[x], {x, 0, nmax}], x]*Range[0, nmax]!] (* _G. C. Greubel_, Sep 16 2018 *)
%o A082308 (PARI) x='x+O('x^30); Vec(serlaplace((1+x)*exp(4*x)*cosh(x))) \\ _G. C. Greubel_, Sep 16 2018
%o A082308 (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!((1+x)*Exp(4*x)*Cosh(x))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Sep 16 2018
%Y A082308 Cf. A082309.
%K A082308 easy,nonn
%O A082308 0,2
%A A082308 _Paul Barry_, Apr 09 2003