OFFSET
0,2
COMMENTS
Old name: Numerators of sequence of fractions with e.g.f. sqrt(1+x)/(1-x).
Denominators are successive powers of 2.
LINKS
Robert Israel, Table of n, a(n) for n = 0..403
FORMULA
b(n) = a(n)/n! satisfies b(n) = (3*b(n-1) + 2*(2*n-3)*b(n-2))/n, b(0)=1, b(1)=3. - Sergei N. Gladkovskii, Jul 22 2012, corrected by Robert Israel, Mar 12 2018
D-finite with recurrence: a(n+2) = (2*(n+1))*(1+2*n)*a(n)+3*a(n+1). - Robert Israel, Mar 12 2018
E.g.f.: sqrt(1+2*x)/(1-2*x). - Sergei N. Gladkovskii, Jul 22 2012
EXAMPLE
The fractions are 1, 3/2, 11/4, 69/8, 537/16, 5475/32, 64755/64, 916965/128, ...
MAPLE
f:= gfun:-rectoproc({-2*(n+1)*(1+2*n)*a(n)-3*a(n+1)+a(n+2), a(0)=1, a(1)=3}, a(n), remember):
map(f, [$0..30]); # Robert Israel, Mar 12 2018
MATHEMATICA
With[{nn=20}, CoefficientList[Series[Sqrt[1+2x]/(1-2x), {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Sep 21 2018 *)
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Mar 22 2007
EXTENSIONS
Better name by Sergei N. Gladkovskii, Jul 22 2012
Edited by Robert Israel, Mar 12 2018
STATUS
approved