A081566 Second binomial transform of expansion of exp(3cosh(x)).

1, 2, 7, 26, 118, 572, 3127, 18146, 114793, 765602, 5463982, 40870436, 323326813, 2667777842, 23092966267, 207651618746, 1947316349278, 18906249136892, 190564801592107, 1982986181092226, 21345005629846213, 236628248493001202

Offset: 0

Author

Paul Barry, Mar 22 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A081565.

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)+2*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)+2*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] + 2 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)+2*x-3) )) \\ G. C. Greubel, Aug 13 2019

Sage

[factorial(n)*( exp(3*cosh(x)+2*x-3) ).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(3*cosh(x))/e^3 = exp(3*cosh(x)+2*x-3).