A081443 Binomial transform of expansion of cosh(sinh(x)).

1, 1, 2, 4, 12, 36, 128, 456, 1872, 7888, 37600, 184064, 990784, 5444544, 32333824, 195982208, 1272660224, 8441139456, 59527313920, 428299217920, 3252626013184, 25165446157312, 204354574172160, 1689266143553536, 14594815769038848

Offset

0,3

Comments

Binomial transform of A003709 (unsigned, with periodic zeros added).

Links

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

Formula

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

Maple

seq(coeff(series(exp(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[x]Cosh[Sinh[x]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Nov 14 2011 *)

Prog

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

Crossrefs

Cf. A003709, A081444.

Sequence in context: A148211 A369688 A009152 * A086647 A268600 A187119

Adjacent sequences: A081440 A081441 A081442 * A081444 A081445 A081446

Keyword

easy,nonn

Author

Paul Barry, Mar 22 2003

Status

approved