A081922 Expansion of exp(4x)/sqrt(1-x^2).

1, 4, 17, 76, 361, 1844, 10321, 64348, 453329, 3619684, 32666161, 329434604, 3677682937, 44901581716, 595567550321, 8505627039484, 130307878338721, 2126927187154628, 36912563369550289, 677277819029706124

Offset

0,2

Comments

Binomial transform of A081921

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

Links

Table of n, a(n) for n=0..19.

Formula

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

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

a(n) ~ n^n * (exp(4) + (-1)^n*exp(-4)) / exp(n). - Vaclav Kotesovec, Feb 04 2014

Mathematica

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

Crossrefs

Cf. A081919, A081920, A081921.

Sequence in context: A005572 A202879 A333059 * A124325 A151248 A104455

Adjacent sequences: A081919 A081920 A081921 * A081923 A081924 A081925

Keyword

easy,nonn

Author

Paul Barry, Apr 01 2003

Status

approved