%I #12 Sep 08 2022 08:45:09
%S 1,1,3,7,27,91,423,1807,9747,49651,303183,1777447,12072987,79587691,
%T 593485623,4327497727,35069154147,279393234211,2440577314143,
%U 21043100301847,196825339400427,1822706292362011,18153886768953543
%N Binomial transform of expansion of exp(2cosh(x)), A000807.
%H Vincenzo Librandi, <a href="/A081562/b081562.txt">Table of n, a(n) for n = 0..200</a>
%F E.g.f.: exp(x)+exp(2*cosh(x))/e^2 = exp(2*cosh(x)+x-2).
%p seq(coeff(series(exp(2*cosh(x)+x-2), x, n+1)*factorial(n), x, n), n = 0 .. 30); # _G. C. Greubel_, Aug 13 2019
%t With[{nn = 30}, CoefficientList[Series[Exp[2 Cosh[x] + x - 2], {x, 0, nn}], x] Range[0, nn]!] (* _Vincenzo Librandi_, Aug 08 2013 *)
%o (PARI) my(x='x+O('x^30)); Vec(serlaplace( exp(2*cosh(x)+x-2) )) \\ _G. C. Greubel_, Aug 13 2019
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(2*Cosh(x)+x-2) )); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Aug 13 2019
%o (Sage) [factorial(n)*( exp(2*cosh(x)+x-2) ).series(x,n+1).list()[n] for n in (0..30)] # _G. C. Greubel_, Aug 13 2019
%Y Cf. A000807, A081563.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Mar 22 2003