A centered triangular number is a centered polygonal number consisting of a central dot surrounded by concentrictriangles,
where
is a nonnegative integer and the th triangle contains dots for . The th term is , and the first few such numbers for , 1, 2, ... are 1, 4, 10, 19, 31, 46, 64, ... (OEIS A005448).
The generating function giving the centered
triangular numbers, convergent for , is
concentric triangles,
where 
is a nonnegative integer and the 
th triangle contains 
dots for 
. The 
th term is 
, and the first few such numbers for 
, 1, 2, ... are 1, 4, 10, 19, 31, 46, 64, ... (OEIS A005448).
The generating function giving the centered
triangular numbers, convergent for 
, is
