OFFSET
0,2
COMMENTS
Denominators are successive powers of 2.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
E.g.f.: (1+2*x)/(1-2*x)^(3/2)
From Sergei N. Gladkovskii, Jul 23 2012: (Start)
a(n) = (4*n+1)*((2*n)!)/( n!*(2^n) ).
G.f.: 3*Q(0), where Q(k)= 1 - (2*k+2)/(3*(2*k+1) - 9*x*(2*k+1)^2*(2*k+3)/(3*x*(2*k+1)*(2*k+3) - (2*k+2)/Q(k+1))); (continued fraction, 3rd kind, 3-step).
(End).
a(n) ~ 2^(n+5/2) * n^(n+1) / exp(n). - Vaclav Kotesovec, Feb 25 2014
EXAMPLE
The fractions are 1, 5/2, 27/4, 195/8, 1785/16, 19845/32, 259875/64, ...
MATHEMATICA
CoefficientList[Series[(1+2*x)/(1-2*x)^(3/2), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Feb 25 2014 *)
PROG
(PARI) {a(n)= if(n<0, 0, n!* polcoeff( (1+2*x)/ (1-2*x +x*O(x^n))^(3/2), n))} /* Michael Somos, Apr 08 2007 */
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Mar 22 2007
STATUS
approved