A081558 Exponential generating function: exp(cosh(x)+2*x-1).

1, 2, 5, 14, 44, 152, 575, 2354, 10379, 48902, 245240, 1301984, 7294589, 42959282, 265263185, 1712168654, 11528506124, 80783015192, 588097479635, 4439382164114, 34699233959759, 280381494540182, 2339287666524440, 20125268756209664, 178348602246900569

Offset: 0

Author

Paul Barry, Mar 22 2003

Keywords

• easy
• nonn

Comments

Old definition was "Second binomial transform of expansion of exp(cosh(x))".

Binomial transform of A081557.

Links

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

Crossrefs

Cf. A005046, A081557.

Programs

Magma

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

Sage

[factorial(n)*( exp(cosh(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(x))/e.

Extensions

Definition edited by N. J. A. Sloane, Dec 12 2021