A228832 Triangle defined by T(n,k) = binomial(n*k, k^2), for n>=0, k=0..n, as read by rows.

1, 1, 1, 1, 2, 1, 1, 3, 15, 1, 1, 4, 70, 220, 1, 1, 5, 210, 5005, 4845, 1, 1, 6, 495, 48620, 735471, 142506, 1, 1, 7, 1001, 293930, 30421755, 183579396, 5245786, 1, 1, 8, 1820, 1307504, 601080390, 40225345056, 69668534468, 231917400, 1, 1, 9, 3060, 4686825, 7307872110, 3169870830126, 96926348578605, 37387265592825, 11969016345, 1

Offset

0,5

Comments

Central coefficients are A201555(n) = C(2*n^2,n^2) = A000984(n^2), where A000984 is the central binomial coefficients.

Links

Paul D. Hanna, Rows 0..30, as a flattened table of n, a(n) for n = 0..495

Example

The triangle of coefficients C(n*k, k^2), n>=k, k=0..n, begins:
1;
1, 1;
1, 2, 1;
1, 3, 15, 1;
1, 4, 70, 220, 1;
1, 5, 210, 5005, 4845, 1;
1, 6, 495, 48620, 735471, 142506, 1;
1, 7, 1001, 293930, 30421755, 183579396, 5245786, 1;
1, 8, 1820, 1307504, 601080390, 40225345056, 69668534468, 231917400, 1;
1, 9, 3060, 4686825, 7307872110, 3169870830126, 96926348578605, 37387265592825, 11969016345, 1; ...

Prog

(PARI) {T(n, k)=binomial(n*k, k^2)}
for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")); print(""))

Crossrefs

Cf. A228808 (row sums), A228833 (antidiagonal sums), A135860 (diagonal), A201555 (central terms).

Cf. A229052.

Cf. related triangles: A228904 (exp), A209330, A226234, A228836.

Sequence in context: A122022 A134357 A049258 * A379217 A247518 A078076

Adjacent sequences: A228829 A228830 A228831 * A228833 A228834 A228835

Keyword

nonn,tabl

Author

Paul D. Hanna, Sep 04 2013

Status

approved