OFFSET
0,2
LINKS
G. C. Greubel, Rows n = 0..50 of the triangle, flattened
FORMULA
T(n, k) = Sum_{j=0..n} (2*n)!/((2*n-k-j)!*j!*k!).
EXAMPLE
Triangle begins as:
1;
3, 4;
11, 28, 24;
42, 156, 225, 160;
163, 792, 1596, 1736, 1120;
638, 3820, 9855, 14400, 13230, 8064;
2510, 17832, 55968, 102520, 122265, 100584, 59136;
9908, 81368, 300482, 661024, 968968, 1005004, 765765, 439296;
MATHEMATICA
Table[Sum[Multinomial[2*n-k-j, k, j], {j, 0, n}], {n, 0, 12}, {k, 0, n}]//Flatten
PROG
(Magma) F:= Factorial; [(&+[F(2*n)/(F(k)*F(j)*F(2*n-k-j)): j in [0..n]]): k in [0..n], n in [0..12]]; // G. C. Greubel, Mar 28 2021
(Sage) f=factorial; flatten([[sum(f(2*n)/(f(k)*f(j)*f(2*n-k-j)) for j in (0..n)) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Mar 28 2021
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Sep 12 2008
EXTENSIONS
Edited by G. C. Greubel, Mar 28 2021
STATUS
approved