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%I #27 Sep 08 2022 08:44:37
%S 1,0,1,6,25,100,481,2954,20721,151848,1146721,9111982,77652169,
%T 710421452,6891125697,69961213170,738718169569,8108554524112,
%U 92647353941569,1101958783026134,13616813607795321,174287243264606388,2304515271134124577,31424734896799742170
%N Expansion of e.g.f. cosh(exp(x)*x).
%H Iain Fox, <a href="/A009121/b009121.txt">Table of n, a(n) for n = 0..541</a>
%p a:= n-> add(`if`(k::odd, 0, binomial(n, k)*k^(n-k)), k=0..n):
%p seq(a(n), n=0..25); # _Alois P. Heinz_, Jan 15 2018
%t With[{nn=30},CoefficientList[Series[Cosh[Exp[x]*x],{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, Dec 28 2015 *)
%o (PARI) first(n) = x='x+O('x^n); Vec(serlaplace(cosh(exp(x)*x))) \\ _Iain Fox_, Dec 23 2017
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cosh(x*Exp(x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Jul 26 2018
%Y Cf. A000248, A009017, A009448, A009565, A009635, A009768.
%K nonn,easy
%O 0,4
%A _R. H. Hardin_
%E Extended and signs tested by _Olivier Gérard_, Mar 15 1997
%E Definition clarified and prior Mathematica program replaced by _Harvey P. Dale_, Dec 28 2015
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