OFFSET
0,2
COMMENTS
Triangle formed of odd-numbered columns of the Delannoy triangle A008288.
LINKS
G. C. Greubel, Rows n = 0..50 of the triangle, flattened
FORMULA
T(2n, n) = A108448(n+1).
Sum_{k=0..n} T(n,k) = A073717(n+1).
From G. C. Greubel, Nov 19 2021: (Start)
T(n, k) = A008288(n+k+1, 2*k+1).
T(n, k) = hypergeometric([-n+k, -2*k-1], [1], 2). (End)
EXAMPLE
Triangle begins
1;
3, 1;
5, 7, 1;
7, 25, 11, 1;
9, 63, 61, 15, 1;
11, 129, 231, 113, 19, 1;
13, 231, 681, 575, 181, 23, 1;
15, 377, 1683, 2241, 1159, 265, 27, 1;
17, 575, 3653, 7183, 5641, 2047, 365, 31, 1;
...
MATHEMATICA
A216182[n_, k_]:= Hypergeometric2F1[-n +k, -2*k-1, 1, 2];
Table[A216182[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Nov 19 2021 *)
PROG
(Sage)
def A216182(n, k): return simplify( hypergeometric([-n+k, -2*k-1], [1], 2) )
flatten([[A216182(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Nov 19 2021
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Philippe Deléham, Mar 11 2013
STATUS
approved