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

0,2

Comments

Periodic zeros suppressed.

Links

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

Formula

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

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 *)

Prog

(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
(Magma) m:=30; R<x>:=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
(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

Crossrefs

Cf. A005046, A081560.

Sequence in context: A301583 A181398 A326274 * A298433 A261042 A002454

Adjacent sequences: A081556 A081557 A081558 * A081560 A081561 A081562

Keyword

easy,nonn

Author

Paul Barry, Mar 22 2003

Extensions

Definition amended by Georg Fischer, Dec 03 2021

Status

approved