login
Expansion of exp(4x)/sqrt(1-x^2).
1

%I #18 Jan 05 2021 21:31:22

%S 1,4,17,76,361,1844,10321,64348,453329,3619684,32666161,329434604,

%T 3677682937,44901581716,595567550321,8505627039484,130307878338721,

%U 2126927187154628,36912563369550289,677277819029706124

%N Expansion of exp(4x)/sqrt(1-x^2).

%C Binomial transform of A081921

%C Generally, if e.g.f. = exp(p*x)/sqrt(1-x^2), then a(n) ~ n^n * (exp(p)+(-1)^n*exp(-p)) / exp(n). - _Vaclav Kotesovec_, Feb 04 2014

%F E.g.f.: exp(4x)/sqrt(1-x^2).

%F D-finite with recurrence: -a(n) + 4*a(n-1) + (n-1)^2*a(n-2) - 4*(n-1)*(n-2)*a(n-3) = 0. - _R. J. Mathar_, Nov 09 2012

%F a(n) ~ n^n * (exp(4) + (-1)^n*exp(-4)) / exp(n). - _Vaclav Kotesovec_, Feb 04 2014

%t With[{nn=20},CoefficientList[Series[Exp[4x]/Sqrt[1-x^2] ,{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, May 07 2012 *)

%Y Cf. A081919, A081920, A081921.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Apr 01 2003