A081560 Binomial transform of expansion of exp(cosh(2*x)).

1, 1, 5, 13, 89, 361, 3005, 16213, 157169, 1048081, 11509685, 90793693, 1108802249, 10054120441, 134712712685, 1375818738853, 20017552431329, 226802388529441, 3554162892847205, 44153857947768493, 740316072791255609

Offset

0,3

Links

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

Formula

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

Maple

seq(coeff(series(exp(cosh(2*x)+x-1), x, n+1)*factorial(n), x, n), n = 0 .. 30); # G. C. Greubel, Aug 13 2019

Mathematica

With[{nn = 200}, CoefficientList[Series[Exp[Cosh[2 x] + x -1], {x, 0, nn}], x] Range[0, nn]!] (* Vincenzo Librandi, Aug 08 2013 *)

Prog

(PARI) my(x='x+O('x^30)); Vec(serlaplace( exp(cosh(2*x)+x-1) )) \\ G. C. Greubel, Aug 13 2019
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(Cosh(2*x)+x-1) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 13 2019
(Sage) [factorial(n)*( exp(cosh(2*x)+x-1) ).series(x, n+1).list()[n] for n in (0..30)] # G. C. Greubel, Aug 13 2019

Crossrefs

Cf. A081559, A081561.

Sequence in context: A190949 A263468 A350467 * A057624 A092567 A055623

Adjacent sequences: A081557 A081558 A081559 * A081561 A081562 A081563

Keyword

easy,nonn

Author

Paul Barry, Mar 22 2003

Status

approved