A081443 Binomial transform of expansion of cosh(sinh(x)).

1, 1, 2, 4, 12, 36, 128, 456, 1872, 7888, 37600, 184064, 990784, 5444544, 32333824, 195982208, 1272660224, 8441139456, 59527313920, 428299217920, 3252626013184, 25165446157312, 204354574172160, 1689266143553536, 14594815769038848

Offset: 0

Author

Paul Barry, Mar 22 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A003709 (unsigned, with periodic zeros added).

Links

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

Crossrefs

Cf. A003709, A081444.

Programs

Magma

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(x)*Cosh(Sinh(x)) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 14 2019

Maple

seq(coeff(series(exp(x)*cosh(sinh(x)), x, n+1)*factorial(n), x, n), n = 0 .. 30); # G. C. Greubel, Aug 14 2019

Mathematica

With[{nn=30},CoefficientList[Series[Exp[x]Cosh[Sinh[x]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Nov 14 2011 *)

PARI

my(x='x+O('x^30)); Vec(serlaplace( exp(x)*cosh(sinh(x)) )) \\ G. C. Greubel, Aug 14 2019

Sage

[factorial(n)*( exp(x)*cosh(sinh(x)) ).series(x,n+1).list()[n] for n in (0..30)] # G. C. Greubel, Aug 14 2019

Formula

E.g.f.: exp(x)*cosh(sinh(x)).