cp's OEIS Frontend

A081560 Binomial transform of expansion of exp(cosh(2*x)).

%I A081560 #12 Sep 08 2022 08:45:09
%S A081560 1,1,5,13,89,361,3005,16213,157169,1048081,11509685,90793693,
%T A081560 1108802249,10054120441,134712712685,1375818738853,20017552431329,
%U A081560 226802388529441,3554162892847205,44153857947768493,740316072791255609
%N A081560 Binomial transform of expansion of exp(cosh(2*x)).
%H A081560 Vincenzo Librandi, <a href="/A081560/b081560.txt">Table of n, a(n) for n = 0..200</a>
%F A081560 E.g.f.: exp(x)*exp(cosh(2*x))/e = exp(cosh(2*x)+x-1).
%p A081560 seq(coeff(series(exp(cosh(2*x)+x-1), x, n+1)*factorial(n), x, n), n = 0 .. 30); # _G. C. Greubel_, Aug 13 2019
%t A081560 With[{nn = 200}, CoefficientList[Series[Exp[Cosh[2 x] + x -1], {x, 0, nn}], x] Range[0, nn]!] (* _Vincenzo Librandi_, Aug 08 2013 *)
%o A081560 (PARI) my(x='x+O('x^30)); Vec(serlaplace( exp(cosh(2*x)+x-1) )) \\ _G. C. Greubel_, Aug 13 2019
%o A081560 (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(Cosh(2*x)+x-1) )); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Aug 13 2019
%o A081560 (Sage) [factorial(n)*( exp(cosh(2*x)+x-1) ).series(x,n+1).list()[n] for n in (0..30)] # _G. C. Greubel_, Aug 13 2019
%Y A081560 Cf. A081559, A081561.
%K A081560 easy,nonn
%O A081560 0,3
%A A081560 _Paul Barry_, Mar 22 2003