A081565 Binomial transform of expansion of exp(3cosh(x)).

1, 1, 4, 10, 49, 181, 1039, 4915, 32134, 182206, 1330609, 8706655, 70012309, 515822581, 4517489344, 36835737130, 348313165249, 3103526872081, 31462900577419, 303344232041215, 3277823503679554, 33930282904263406

Offset

0,3

Comments

Binomial transform of A081564.

Links

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

Formula

E.g.f.: exp(x) * exp(3*cosh(x))/e^3 = exp(3*cosh(x)+x-3).

Maple

seq(coeff(series(exp(3*cosh(x)+x-3), x, n+1)*factorial(n), x, n), n = 0 .. 30); # G. C. Greubel, Aug 13 2019

Mathematica

With[{nn = 30}, CoefficientList[Series[Exp[3 Cosh[x] + x - 3], {x, 0, nn}], x] Range[0, nn]!] (* Vincenzo Librandi, Aug 08 2013 *)

Prog

(PARI) my(x='x+O('x^30)); Vec(serlaplace( exp(3*cosh(x)+x-3) )) \\ G. C. Greubel, Aug 13 2019
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(3*Cosh(x)+x-3) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 13 2019
(Sage) [factorial(n)*( exp(3*cosh(x)+x-3) ).series(x, n+1).list()[n] for n in (0..30)] # G. C. Greubel, Aug 13 2019

Crossrefs

Cf. A081564, A081565.

Sequence in context: A335873 A364281 A173086 * A151611 A351046 A208236

Adjacent sequences: A081562 A081563 A081564 * A081566 A081567 A081568

Keyword

easy,nonn

Author

Paul Barry, Mar 22 2003

Status

approved