A081560 Binomial transform of expansion of exp(cosh(2*x)).
1, 1, 5, 13, 89, 361, 3005, 16213, 157169, 1048081, 11509685, 90793693, 1108802249, 10054120441, 134712712685, 1375818738853, 20017552431329, 226802388529441, 3554162892847205, 44153857947768493, 740316072791255609
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
Programs
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Magma
m:=30; R
:=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 -
Maple
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
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Mathematica
With[{nn = 200}, CoefficientList[Series[Exp[Cosh[2 x] + x -1], {x, 0, nn}], x] Range[0, nn]!] (* Vincenzo Librandi, Aug 08 2013 *) -
PARI
my(x='x+O('x^30)); Vec(serlaplace( exp(cosh(2*x)+x-1) )) \\ G. C. Greubel, Aug 13 2019 -
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
Formula
E.g.f.: exp(x)*exp(cosh(2*x))/e = exp(cosh(2*x)+x-1).
Comments