A081563 Second binomial transform of expansion of exp(2*cosh(x)).

1, 2, 6, 20, 78, 332, 1566, 7940, 43518, 253532, 1573566, 10295540, 71069598, 513897932, 3893187486, 30741656420, 252979075518, 2161184079932, 19161309456126, 175782239098580, 1667967153565278, 16331180476591532

Offset: 0

Author

Paul Barry, Mar 22 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A081562.

Links

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

Crossrefs

Cf. A000807, A081562.

Programs

Magma

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(2*Cosh(x)+2*x-2) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 13 2019

Maple

seq(coeff(series(exp(2*cosh(x)+2*x-2), x, n+1)*factorial(n), x, n), n = 0 .. 30); # G. C. Greubel, Aug 13 2019

Mathematica

With[{nn = 30}, CoefficientList[Series[Exp[2 Cosh[x] + 2 x - 2], {x, 0, nn}], x] Range[0, nn]!] (* Vincenzo Librandi, Aug 08 2013 *)

PARI

my(x='x+O('x^30)); Vec(serlaplace( exp(2*cosh(x)+2*x-2) )) \\ G. C. Greubel, Aug 13 2019

Sage

[factorial(n)*( exp(2*cosh(x)+2*x-2) ).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(2*cosh(x))/e^2 = exp(2*cosh(x)+2*x-2).