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A226234 Triangle defined by T(n,k) = binomial(n^2, k^2), for n>=0, k=0..n, as read by rows. 6
1, 1, 1, 1, 4, 1, 1, 9, 126, 1, 1, 16, 1820, 11440, 1, 1, 25, 12650, 2042975, 2042975, 1, 1, 36, 58905, 94143280, 7307872110, 600805296, 1, 1, 49, 211876, 2054455634, 3348108992991, 63205303218876, 262596783764, 1, 1, 64, 635376, 27540584512, 488526937079580, 401038568751465792, 1118770292985239888, 159518999862720, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
Row sums equal A206849.
Antidiagonal sums equal A123165.
LINKS
EXAMPLE
The triangle of coefficients C(n^2,k^2), n>=k, k=0..n, begins:
1;
1, 1;
1, 4, 1;
1, 9, 126, 1;
1, 16, 1820, 11440, 1;
1, 25, 12650, 2042975, 2042975, 1;
1, 36, 58905, 94143280, 7307872110, 600805296, 1;
1, 49, 211876, 2054455634, 3348108992991, 63205303218876, 262596783764, 1;
1, 64, 635376, 27540584512, 488526937079580, 401038568751465792, 1118770292985239888, 159518999862720, 1; ...
PROG
(PARI) {T(n, k)=binomial(n^2, k^2)}
for(n=0, 9, for(k=0, n, print1(T(n, k), ", ")); print(""))
CROSSREFS
Cf. related triangles: A228902(exp), A209330, A228832, A228836.
Sequence in context: A157108 A056647 A056057 * A369189 A185027 A016520
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Aug 24 2013
STATUS
approved

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Last modified June 20 12:38 EDT 2024. Contains 373527 sequences. (Running on oeis4.)