A081561 Second binomial transform of expansion of exp(cosh(2*x)).

1, 2, 8, 32, 176, 992, 6848, 48512, 398336, 3356672, 31751168, 307914752, 3282292736, 35827392512, 423577223168, 5121571684352, 66347485822976, 877984005619712, 12344359378485248, 177098976447168512

Offset: 0

Author

Paul Barry, Mar 22 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A081560.

Links

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

Crossrefs

Cf. A081559, A081560.

Programs

Magma

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(Cosh(2*x)+2*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)+2*x-1), x, n+1)*factorial(n), x, n), n = 0 .. 30); # G. C. Greubel, Aug 13 2019

Mathematica

With[{nn = 30}, CoefficientList[Series[Exp[Cosh[2 x] + 2 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)+2*x-1) )) \\ G. C. Greubel, Aug 13 2019

Sage

[factorial(n)*( exp(cosh(2*x)+2*x-1) ).series(x,n+1).list()[n] for n in (0..30)] # G. C. Greubel, Aug 13 2019

Formula

E.g.f.: exp(2*x) * exp(cosh(2*x))/e = exp(cosh(2*x)+2*x-1)