%I #14 Sep 08 2022 08:45:09
%S 1,1,4,10,49,181,1039,4915,32134,182206,1330609,8706655,70012309,
%T 515822581,4517489344,36835737130,348313165249,3103526872081,
%U 31462900577419,303344232041215,3277823503679554,33930282904263406
%N Binomial transform of expansion of exp(3cosh(x)).
%C Binomial transform of A081564.
%H Vincenzo Librandi, <a href="/A081565/b081565.txt">Table of n, a(n) for n = 0..200</a>
%F E.g.f.: exp(x) * exp(3*cosh(x))/e^3 = exp(3*cosh(x)+x-3).
%p seq(coeff(series(exp(3*cosh(x)+x-3), x, n+1)*factorial(n), x, n), n = 0 .. 30); # _G. C. Greubel_, Aug 13 2019
%t With[{nn = 30}, CoefficientList[Series[Exp[3 Cosh[x] + x - 3], {x, 0, nn}], x] Range[0, nn]!] (* _Vincenzo Librandi_, Aug 08 2013 *)
%o (PARI) my(x='x+O('x^30)); Vec(serlaplace( exp(3*cosh(x)+x-3) )) \\ _G. C. Greubel_, Aug 13 2019
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(3*Cosh(x)+x-3) )); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Aug 13 2019
%o (Sage) [factorial(n)*( exp(3*cosh(x)+x-3) ).series(x,n+1).list()[n] for n in (0..30)] # _G. C. Greubel_, Aug 13 2019
%Y Cf. A081564, A081565.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Mar 22 2003