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 A228832 Triangle defined by T(n,k) = binomial(n*k, k^2), for n>=0, k=0..n, as read by rows. 12
 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 (list; table; graph; refs; listen; history; text; internal format)
 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 * A247518 A078076 A010247 Adjacent sequences:  A228829 A228830 A228831 * A228833 A228834 A228835 KEYWORD nonn,tabl AUTHOR Paul D. Hanna, Sep 04 2013 STATUS approved

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Last modified February 29 05:25 EST 2020. Contains 332353 sequences. (Running on oeis4.)