A081443 Binomial transform of expansion of cosh(sinh(x)).
1, 1, 2, 4, 12, 36, 128, 456, 1872, 7888, 37600, 184064, 990784, 5444544, 32333824, 195982208, 1272660224, 8441139456, 59527313920, 428299217920, 3252626013184, 25165446157312, 204354574172160, 1689266143553536, 14594815769038848
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(x)*Cosh(Sinh(x)) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 14 2019 -
Maple
seq(coeff(series(exp(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[x]Cosh[Sinh[x]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Nov 14 2011 *) -
PARI
my(x='x+O('x^30)); Vec(serlaplace( exp(x)*cosh(sinh(x)) )) \\ G. C. Greubel, Aug 14 2019 -
Sage
[factorial(n)*( exp(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(x)*cosh(sinh(x)).
Comments