OFFSET
0,4
COMMENTS
FORMULA
G.f.: (1 - x + x^2)/(1 - 2*x - x*y + x^2).
T(n,k) = 2*T(n-1,k) + T(n-1,k-1) - T(n-2,k), T(0,0) = T(1,0) = T(1,1) = 1, T(2,0) = 2, T(2,1) = 3, T(2,2) = 1, T(n,k) = 0 if k < 0 or k > n.
The Riordan square (see A321620) of 1 + x/(1 - x)^2. - Peter Luschny, Mar 06 2022
EXAMPLE
Triangle begins:
1;
1, 1;
2, 3, 1;
3, 7, 5, 1;
4, 14, 16, 7, 1;
5, 25, 41, 29, 9, 1;
6, 41, 91, 92, 46, 11, 1;
7, 63, 182, 246, 175, 67, 13, 1;
MAPLE
# The function RiordanSquare is defined in A321620.
RiordanSquare(1+x/(1-x)^2, 8); # Peter Luschny, Mar 06 2022
MATHEMATICA
CoefficientList[#, y] & /@
CoefficientList[
Series[(1 - x + x^2)/(1 - 2*x - x*y + x^2), {x, 0, 12}], x] (* Wouter Meeussen, Jan 25 2014 *)
CROSSREFS
Cf. A321620.
KEYWORD
nonn,tabl
AUTHOR
Philippe Deléham, Jan 24 2014
STATUS
approved