A081559 Expansion of e.g.f.: exp(cosh(2*x)-1), even powers only.

1, 4, 64, 1984, 97024, 6713344, 615829504, 71654785024, 10243143368704, 1755968011239424, 354197952894337024, 82788022987201183744, 22140953727834378993664, 6703959915806302859689984, 2277487386474356139699994624, 861378969099073547571187154944

Offset: 0

Author

Paul Barry, Mar 22 2003

Keywords

• easy
• nonn

Comments

Periodic zeros suppressed.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A005046, A081560.

Programs

Magma

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

Maple

seq(coeff(series(exp(cosh(2*x)-1), x, 2*n+1)*factorial(2*n), x, 2*n), n = 0 .. 15); # G. C. Greubel, Aug 13 2019

Mathematica

With[{nn = 30}, CoefficientList[Series[Exp[Cosh[2*x]-1], {x, 0, nn}], x] Range[0, nn]!][[1 ;; ;; 2]] (* G. C. Greubel, Aug 13 2019 *)

PARI

my(x='x+O('x^30)); v=Vec(serlaplace( exp(cosh(2*x)-1) )); vector(#v\2, n, v[2*n-1]) \\ G. C. Greubel, Aug 13 2019

Sage

[factorial(2*n)*( exp(cosh(2*x)-1) ).series(x, 2*n+1).list()[2*n] for n in (0..15)] # G. C. Greubel, Aug 13 2019

Formula

E.g.f.: exp(cosh(2*x))/e = exp(cosh(2*x)-1).

Extensions

Definition amended by Georg Fischer, Dec 03 2021