A081562 Binomial transform of expansion of exp(2cosh(x)), A000807.

1, 1, 3, 7, 27, 91, 423, 1807, 9747, 49651, 303183, 1777447, 12072987, 79587691, 593485623, 4327497727, 35069154147, 279393234211, 2440577314143, 21043100301847, 196825339400427, 1822706292362011, 18153886768953543

Offset: 0

Author

Paul Barry, Mar 22 2003

Keywords

• easy
• nonn

Links

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

Crossrefs

Cf. A000807, A081563.

Programs

Magma

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

Sage

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

Formula

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