A081565 Binomial transform of expansion of exp(3cosh(x)).

1, 1, 4, 10, 49, 181, 1039, 4915, 32134, 182206, 1330609, 8706655, 70012309, 515822581, 4517489344, 36835737130, 348313165249, 3103526872081, 31462900577419, 303344232041215, 3277823503679554, 33930282904263406

Offset: 0

Author

Paul Barry, Mar 22 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A081564.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A081564, A081565.

Programs

Magma

m:=30; R:=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

Maple

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

Mathematica

With[{nn = 30}, CoefficientList[Series[Exp[3 Cosh[x] + x - 3], {x, 0, nn}], x] Range[0, nn]!] (* Vincenzo Librandi, Aug 08 2013 *)

PARI

my(x='x+O('x^30)); Vec(serlaplace( exp(3*cosh(x)+x-3) )) \\ G. C. Greubel, Aug 13 2019

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

Formula

E.g.f.: exp(x) * exp(3*cosh(x))/e^3 = exp(3*cosh(x)+x-3).