A228836 Triangle defined by T(n,k) = binomial(n^2, (n-k)*k), for n>=0, k=0..n, as read by rows.

1, 1, 1, 1, 4, 1, 1, 36, 36, 1, 1, 560, 1820, 560, 1, 1, 12650, 177100, 177100, 12650, 1, 1, 376992, 30260340, 94143280, 30260340, 376992, 1, 1, 13983816, 8217822536, 92263734836, 92263734836, 8217822536, 13983816, 1, 1, 621216192, 3284214703056, 159518999862720, 488526937079580

Offset

0,5

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^2, (n-k)*k), n>=k, k=0..n, begins:
1;
1, 1;
1, 4, 1;
1, 36, 36, 1;
1, 560, 1820, 560, 1;
1, 12650, 177100, 177100, 12650, 1;
1, 376992, 30260340, 94143280, 30260340, 376992, 1;
1, 13983816, 8217822536, 92263734836, 92263734836, 8217822536, 13983816, 1;
1, 621216192, 3284214703056, 159518999862720, 488526937079580, 159518999862720, 3284214703056, 621216192, 1; ...

Prog

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

Crossrefs

Cf. A207136 (row sums), A228837 (antidiagonal sums), A070780 (column 1).

Cf. related triangles: A228900(exp), A209330, A226234, A228832.

Sequence in context: A177939 A209196 A158390 * A176419 A299471 A102602

Adjacent sequences: A228833 A228834 A228835 * A228837 A228838 A228839

Keyword

nonn,tabl

Author

Paul D. Hanna, Sep 05 2013

Status

approved