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
Links
- G. C. Greubel, Table of n, a(n) for n = 0..445
Crossrefs
Cf. A081440.
Programs
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Magma
m:=30; R
:=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 -
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
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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 *) -
PARI
my(x='x+O('x^30)); Vec(serlaplace( exp(2*x)*cosh(x/sqrt(1-x^2)) )) \\ 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
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
Comments