A081566 Second binomial transform of expansion of exp(3cosh(x)).

1, 2, 7, 26, 118, 572, 3127, 18146, 114793, 765602, 5463982, 40870436, 323326813, 2667777842, 23092966267, 207651618746, 1947316349278, 18906249136892, 190564801592107, 1982986181092226, 21345005629846213, 236628248493001202

Offset

0,2

Comments

Binomial transform of A081565.

Links

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

Formula

E.g.f.: exp(2*x) * exp(3*cosh(x))/e^3 = exp(3*cosh(x)+2*x-3).

Maple

seq(coeff(series(exp(3*cosh(x)+2*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] + 2 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)+2*x-3) )) \\ G. C. Greubel, Aug 13 2019
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(3*Cosh(x)+2*x-3) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 13 2019
(Sage) [factorial(n)*( exp(3*cosh(x)+2*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: A309396 A218670 A302691 * A213094 A141203 A346749

Adjacent sequences: A081563 A081564 A081565 * A081567 A081568 A081569

Keyword

easy,nonn

Author

Paul Barry, Mar 22 2003

Status

approved