OFFSET
0,3
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: (x^2 - (sqrt(1-4*x)+2)*x + 1)/(sqrt(1-4*x)*(x-1)^2). - Harvey P. Dale, Apr 18 2014
D-finite with recurrence: n*a(n) + (-7*n+5)*a(n-1) + 3*(5*n-8)*a(n-2) + (-13*n+33)*a(n-3) + 2*(2*n-7)*a(n-4) = 0. - R. J. Mathar, Jan 28 2020
EXAMPLE
a(3)=17 since can map (1,2,3) to (1,1,1), (1,1,2), (1,1,3), (1,2,2), (1,2,3), (1,3,3), (2,1,1), (2,2,1), (2,2,2), (2,2,3), (2,3,3), (3,1,1), (3,2,1), (3,2,2), (3,3,1), (3,3,2), or (3,3,3) but not for example to (1,3,2).
MATHEMATICA
Table[Binomial[2n, n]-n, {n, 0, 30}] (* or *) CoefficientList[Series[ (x^2- (Sqrt[1-4 x]+2) x+1)/(Sqrt[1-4 x] (x-1)^2), {x, 0, 30}], x] (* Harvey P. Dale, Apr 18 2014 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved