A081440 Expansion of e.g.f.: exp(x)*cosh(x/sqrt(1 - x^2)).

1, 1, 2, 4, 20, 76, 632, 3424, 38096, 265360, 3682592, 31332544, 520705088, 5232870592, 101265169280, 1173634791424, 25911499036928, 340187621683456, 8436057652027904, 123731966851240960, 3404264757518332928

Offset

0,3

Comments

First binomial transform of expansion of cosh(x/sqrt(1-x^2)).

Links

G. C. Greubel, Table of n, a(n) for n = 0..445

Formula

D-finite with recurrence: a(n) = 2*a(n-1) + 3*(n-2)^2*a(n-2) - 3*(n-2)*(2*n-5)*a(n-3) - 3*(n-3)*(n-2)*(n^2 - 7*n + 11)*a(n-4) + 6*(n-4)^2*(n-3)*(n-2)*a(n-5) + (n-7)*(n-5)*(n-4)*(n-3)^2*(n-2)*a(n-6) - (n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(2*n-11)*a(n-7) + (n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*a(n-8). - Vaclav Kotesovec, Oct 29 2014

Maple

seq(coeff(series(exp(x)*cosh(x/sqrt(1-x^2)), x, n+1)*factorial(n), x, n), n = 0 .. 25); # G. C. Greubel, Aug 14 2019

Mathematica

With[{nn=25}, CoefficientList[Series[Exp[x]Cosh[x/Sqrt[1-x^2]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jun 05 2014 *)

Prog

(PARI) my(x='x+O('x^25)); Vec(serlaplace( exp(x)*cosh(x/sqrt(1-x^2)) )) \\ G. C. Greubel, Aug 14 2019
(Magma) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(x)*Cosh(x/Sqrt(1-x^2)) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 14 2019
(Sage) [factorial(n)*( exp(x)*cosh(x/sqrt(1-x^2)) ).series(x, n+1).list()[n] for n in (0..25)] # G. C. Greubel, Aug 14 2019

Crossrefs

Cf. A081439, A081442.

Sequence in context: A279153 A204550 A009291 * A204438 A325791 A188326

Adjacent sequences: A081437 A081438 A081439 * A081441 A081442 A081443

Keyword

easy,nonn

Author

Paul Barry, Mar 21 2003

Extensions

Definition clarified by Harvey P. Dale, Jun 05 2014

Status

approved