A081557 Binomial transform of expansion of exp(cosh(x)), A005046.

1, 1, 2, 4, 11, 31, 107, 379, 1556, 6556, 31007, 150349, 801341, 4373461, 25853102, 156297964, 1012382291, 6698486371, 47089993967, 337789490599, 2557480572656, 19738202807236, 159928950077327, 1319703681935929, 11382338060040761, 99896787342523081

Offset

0,3

Links

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

Formula

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

Maple

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

Mathematica

With[{nn = 30}, CoefficientList[Series[Exp[Cosh[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(x)+x-1) )) \\ G. C. Greubel, Aug 13 2019
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(Cosh(x)+x-1) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 13 2019
(Sage) [factorial(n)*( exp(cosh(x)+x-1) ).series(x, n+1).list()[n] for n in (0..30)] # G. C. Greubel, Aug 13 2019

Crossrefs

Cf. A081558.

Sequence in context: A275426 A115625 A056323 * A154603 A063254 A280766

Adjacent sequences: A081554 A081555 A081556 * A081558 A081559 A081560

Keyword

easy,nonn

Author

Paul Barry, Mar 22 2003

Status

approved