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
Links
- G. C. Greubel, Table of n, a(n) for n = 0..445
Programs
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Magma
m:=25; R
:=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 -
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
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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 *) -
PARI
my(x='x+O('x^25)); Vec(serlaplace( exp(x)*cosh(x/sqrt(1-x^2)) )) \\ 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
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
Extensions
Definition clarified by Harvey P. Dale, Jun 05 2014
Comments