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 A174158 Triangle read by rows: T(n,m) = (binomial(n - 1, m - 1)*binomial(n, m - 1)/m)^2. 3
 1, 1, 1, 1, 9, 1, 1, 36, 36, 1, 1, 100, 400, 100, 1, 1, 225, 2500, 2500, 225, 1, 1, 441, 11025, 30625, 11025, 441, 1, 1, 784, 38416, 240100, 240100, 38416, 784, 1, 1, 1296, 112896, 1382976, 3111696, 1382976, 112896, 1296, 1, 1, 2025, 291600, 6350400, 28005264, 28005264, 6350400, 291600, 2025, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS Stefano Spezia, First 150 rows of the triangle, flattened Abderrahim Arabi, HacĂ¨ne Belbachir, and Jean-Philippe Dubernard, Enumeration of parallelogram polycubes, arXiv:2105.00971 [cs.DM], 2021. FORMULA T(n,m) = (binomial(n - 1, m - 1)*binomial(n, m - 1)/m)^2. T(n,m) = A001263(n,m)^2. T(n,m) = A000290(A007318(n - 1, m - 1)*A007318(n, m - 1)/m). - Stefano Spezia, Dec 23 2018 EXAMPLE n\m | 1         2         3         4         5         6         7 ----|--------------------------------------------------------------   1 | 1   2 | 1         1   3 | 1         9         1   4 | 1        36        36         1   5 | 1       100       400       100         1   6 | 1       225      2500      2500       225         1   7 | 1       441     11025     30625     11025       441         1 MAPLE a := (n, m) -> binomial(n-1, m-1)^2*binomial(n, m-1)^2/m^2: seq(seq(a(n, m), m = 1 .. n), n = 1 .. 10) # Stefano Spezia, Dec 23 2018 MATHEMATICA T[n_, m_] = (Binomial[n - 1, m - 1]*Binomial[n, m - 1]/m)^2; Flatten[Table[Table[t[n, m], {m, 1, n}], {n, 1, 10}]] PROG (GAP) Flat(List([1..10], n->List([1..n], m->(Binomial(n-1, m-1)*Binomial(n, m-1)/m)^2))); # Stefano Spezia, Dec 23 2018 (PARI) T(n, m)= (binomial(n-1, m-1)*binomial(n, m-1)/m)^2; tabl(nn) = for(n=1, nn, for(m=1, n, print1(T(n, m), ", ")); print); tabl(10) \\ Stefano Spezia, Dec 23 2018 CROSSREFS Cf. A001263 (Narayana numbers), A007318. Cf. A319743 (row sums). Sequence in context: A073702 A171822 A176490 * A181144 A142468 A304321 Adjacent sequences:  A174155 A174156 A174157 * A174159 A174160 A174161 KEYWORD nonn,tabl,changed AUTHOR Roger L. Bagula, Mar 10 2010 EXTENSIONS Edited by Stefano Spezia, Dec 23 2018 STATUS approved

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Last modified May 6 00:41 EDT 2021. Contains 343579 sequences. (Running on oeis4.)