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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 Paul D. Hanna, Rows n = 0..30, as a flattened table of n, a(n) for n = 0..495 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. A206849, A123165. Cf. related triangles: A228902(exp), A209330, A228832, A228836. Sequence in context: A157108 A056647 A056057 * A369189 A185027 A016520 Adjacent sequences: A226231 A226232 A226233 * A226235 A226236 A226237 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.)