A081439 Expansion of exp(2*x)*cosh(x/sqrt(1 - x^2)).

1, 2, 5, 14, 53, 242, 1505, 10334, 89129, 797090, 8618045, 94186094, 1220350301, 15745031954, 237660317081, 3534411032894, 60889488170321, 1025300949710402, 19847126167227509, 373194859437512654, 8017708459752349061

Offset

0,2

Comments

Second 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) = 4*a(n-1) + 3*(n-3)*(n-1)*a(n-2) - 6*(n-2)*(2*n-5)*a(n-3) - 3*(n-3)*(n-2)*(n^2 - 7*n + 8)*a(n-4) + 12*(n-4)^2*(n-3)*(n-2)*a(n-5) + (n-5)*(n-4)*(n-3)*(n-2)*(n^2 - 10*n + 12)*a(n-6) - 2*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(2*n-11)*a(n-7) + 4*(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(2*x)*cosh(x/sqrt(1-x^2)), x, n+1)*factorial(n), x, n), n = 0 .. 30); # G. C. Greubel, Aug 14 2019

Mathematica

With[{nn=20}, CoefficientList[Series[Exp[2*x]*Cosh[x/Sqrt[1-x^2]], {x, 0, nn}], x] * Range[0, nn]!] (* Vaclav Kotesovec, Oct 29 2014 *)

Prog

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

Crossrefs

Cf. A081440.

Sequence in context: A266932 A243787 A275825 * A052649 A267561 A267560

Adjacent sequences: A081436 A081437 A081438 * A081440 A081441 A081442

Keyword

easy,nonn

Author

Paul Barry, Mar 21 2003

Status

approved