A081444 Second binomial transform of expansion of cosh(sinh(x)).

1, 2, 5, 14, 45, 162, 641, 2718, 12249, 58370, 294493, 1571374, 8858053, 52542882, 326804185, 2122860862, 14366452913, 101063123202, 738075208501, 5587492946510, 43795838894941, 354876969914786, 2968890716640945

Offset

0,2

Comments

Second binomial transform of A003709 (viewed as unsigned, with periodic zeros added).

Binomial transform of A081443.

Links

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

Formula

E.g.f.: exp(2*x) * cosh(sinh(x)).

Maple

seq(coeff(series(exp(2*x)*cosh(sinh(x)), x, n+1)*factorial(n), x, n), n = 0 .. 30); # G. C. Greubel, Aug 14 2019

Mathematica

With[{nn = 30}, CoefficientList[Series[Exp[2x]Cosh[Sinh[x]], {x, 0, nn}], x] Range[0, nn]!] (* Vincenzo Librandi, Aug 08 2013 *)

Prog

(PARI) my(x='x+O('x^30)); Vec(serlaplace( exp(2*x)*cosh(sinh(x)) )) \\ G. C. Greubel, Aug 14 2019
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(2*x)*Cosh(Sinh(x)) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 14 2019
(Sage) [factorial(n)*( exp(2*x)*cosh(sinh(x)) ).series(x, n+1).list()[n] for n in (0..30)] # G. C. Greubel, Aug 14 2019

Crossrefs

Sequence in context: A149893 A149894 A030126 * A268004 A119429 A290615

Adjacent sequences: A081441 A081442 A081443 * A081445 A081446 A081447

Keyword

easy,nonn

Author

Paul Barry, Mar 22 2003

Status

approved