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Expansion of e.g.f. x*exp(5*x)*cosh(x).
5

%I #12 Sep 08 2022 08:45:09

%S 0,1,10,78,560,3880,26400,177632,1185280,7853184,51699200,338331136,

%T 2201948160,14258137088,91894620160,589744496640,3770069811200,

%U 24015941435392,152494553825280,965472423378944,6096346179174400

%N Expansion of e.g.f. x*exp(5*x)*cosh(x).

%C Binomial transform of A082135. 5th binomial transform of (0,1,0,3,0,5,0,7,...)

%H G. C. Greubel, <a href="/A082136/b082136.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) = n*(4^(n-1) + 6^(n-1))/2.

%F E.g.f.: x*exp(5*x)*cosh(x).

%F G.f. x*(1-10*x+26*x^2) / ( (6*x-1)^2*(4*x-1)^2 ). - _R. J. Mathar_, Nov 24 2012

%t With[{nmax = 50}, CoefficientList[Series[x*Exp[5*x]*Cosh[x], {x, 0, nmax}], x]*Range[0, nmax]!] (* or *) Table[n*(4^(n-1)+6^(n-1))/2, {n,0,30}] (* _G. C. Greubel_, Feb 05 2018 *)

%o (PARI) for(n=0,30, print1(n*(4^(n-1)+6^(n-1))/2, ", ")) \\ _G. C. Greubel_, Feb 05 2018

%o (Magma) [n*(4^(n-1)+6^(n-1))/2: n in [0..30]]; // _G. C. Greubel_, Feb 05 2018

%Y Cf. A082134.

%K easy,nonn

%O 0,3

%A _Paul Barry_, Apr 06 2003