A081444 Second binomial transform of expansion of cosh(sinh(x)).
1, 2, 5, 14, 45, 162, 641, 2718, 12249, 58370, 294493, 1571374, 8858053, 52542882, 326804185, 2122860862, 14366452913, 101063123202, 738075208501, 5587492946510, 43795838894941, 354876969914786, 2968890716640945
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(2*x)*Cosh(Sinh(x)) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 14 2019 -
Maple
seq(coeff(series(exp(2*x)*cosh(sinh(x)), x, n+1)*factorial(n), x, n), n = 0 .. 30); # G. C. Greubel, Aug 14 2019
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Mathematica
With[{nn = 30}, CoefficientList[Series[Exp[2x]Cosh[Sinh[x]], {x, 0, nn}], x] Range[0, nn]!] (* Vincenzo Librandi, Aug 08 2013 *) -
PARI
my(x='x+O('x^30)); Vec(serlaplace( exp(2*x)*cosh(sinh(x)) )) \\ G. C. Greubel, Aug 14 2019 -
Sage
[factorial(n)*( exp(2*x)*cosh(sinh(x)) ).series(x,n+1).list()[n] for n in (0..30)] # G. C. Greubel, Aug 14 2019
Formula
E.g.f.: exp(2*x) * cosh(sinh(x)).
Comments