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A228836 Triangle defined by T(n,k) = binomial(n^2, (n-k)*k), for n>=0, k=0..n, as read by rows. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified February 19 03:53 EST 2020. Contains 332031 sequences. (Running on oeis4.)