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A141723
Triangle T(n, k) = Sum_{j=0..n} (2*n)!/((2*n-k-j)!*j!*k!), read by rows.
1
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, 39203, 365104, 1549320, 3975440, 6910540, 8653008, 8112104, 5845840, 3294720
OFFSET
0,2
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
Sequence in context: A198443 A041231 A042129 * A268478 A180363 A100845
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Sep 12 2008
EXTENSIONS
Edited by G. C. Greubel, Mar 28 2021
STATUS
approved