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%I #23 Sep 08 2022 08:44:37
%S 1,0,1,3,12,30,180,490,5600,8064,276360,-575872,22950576,-166106512,
%T 3194871680,-38456524080,663548916992,-10330038449792,186243968575488,
%U -3385894106098944,66478140305126272,-1354838641265098752
%N Expansion of e.g.f. cosh(log(1+x)*exp(x)).
%H Vincenzo Librandi, <a href="/A009135/b009135.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) ~ (-1)^n * n! / (2 * Gamma(exp(-1)) * n^(1 - exp(-1))). - _Vaclav Kotesovec_, Jul 28 2018
%t With[{nn=30},CoefficientList[Series[Cosh[Log[1+x]*Exp[x]],{x,0,nn}], x]Range[0,nn]!] (* _Harvey P. Dale_, Nov 29 2011 *)
%o (PARI) x='x+O('x^30); Vec(serlaplace(cosh(log(1+x)*exp(x)))) \\ _G. C. Greubel_, Jul 28 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cosh(Log(1+x)*Exp(x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Jul 28 2018
%K sign,easy
%O 0,4
%A _R. H. Hardin_
%E Extended with signs by _Olivier Gérard_, Mar 15 1997
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