OFFSET
0,3
COMMENTS
Every term after the second is a multiple of 5.
REFERENCES
M. Kauers and P. Paule, The Concrete Tetrahedron, Springer 2011, p. 41.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: 2 - sqrt(1 - x - x^2) for the fractions (not the numerators).
EXAMPLE
The Maclaurin series begins with 1 + (1/2)*x + (5/8)*x^2 + (5/16)*x^3 + ....
MATHEMATICA
Numerator[CoefficientList[Series[2-Sqrt[1-x-x^2], {x, 0, 30}], x]] (* G. C. Greubel, Jan 25 2019 *)
PROG
(PARI) my(x='x+O('x^30)); v=Vec( 2-sqrt(1-x-x^2) ); vector(#v, n, numerator(v[n])) \\ G. C. Greubel, Jan 25 2019
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( 2-Sqrt(1-x-x^2) )); [Numerator(Factorial(n-1)*b[n]): n in [1..m]]; // G. C. Greubel, Jan 25 2019
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Clark Kimberling, Jun 04 2010
STATUS
approved