OFFSET
0,3
COMMENTS
FORMULA
G.f.: (1-x)/(1-2*x*(1+y)+x^2*(1-y)^2).
T(n,k) = 2*T(n-1,k)+2*T(n-1,k-1)+2*T(n-2,k-1)-T(n-2,k)-T(n-2,k-2), T(0,0)=T(1,0)=1, T(1,1)=2, T(n,k)=0 if k<0 or if k>n.
T(n,k) = binomial(2*n,2*k)*(2*n+1-k)/(2*n+1-2*k). - Peter Luschny, Nov 26 2013
EXAMPLE
Triangle begins:
1
1, 2
1, 8, 3
1, 18, 25, 4
1, 32, 98, 56, 5
1, 50, 270, 336, 105, 6
1, 72, 605, 1320, 891, 176, 7
1, 98, 1183, 4004, 4719, 2002, 273, 8
1, 128, 2100, 10192, 18590, 13728, 4004, 400, 9
MAPLE
T := (n, k) -> binomial(2*n, 2*k)*(2*n+1-k)/(2*n+1-2*k);
seq(seq(T(n, k), k=0..n), n=0..9); # Peter Luschny, Nov 26 2013
MATHEMATICA
Flatten[Table[(Binomial[2n, 2k]+Binomial[2n+1, 2k])/2, {n, 0, 10}, {k, 0, n}]] (* Harvey P. Dale, Jul 05 2015 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Philippe Deléham, Nov 25 2013
STATUS
approved