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 A039797 Triangle of numbers of Dyck paths. 1
 1, 1, 1, 3, 3, 1, 14, 14, 6, 1, 84, 84, 40, 10, 1, 594, 594, 300, 90, 15, 1, 4719, 4719, 2475, 825, 175, 21, 1, 40898, 40898, 22022, 7865, 1925, 308, 28, 1, 379236, 379236, 208208, 78078, 21021, 4004, 504, 36, 1, 3711916, 3711916, 2068560, 804440, 231868, 49686, 7644, 780, 45, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS D. Gouyou-Beauchamps, Chemins sous-diagonaux et tableau de Young, pp. 112-125 of "Combinatoire Enumérative (Montreal 1985)", Lect. Notes Math. 1234, 1986. FORMULA T(n, k) = (2n-k)!*(2n-k+2)!*(k+3)!/((n-k)!*(n-k+1)!*k!*(n+2)!*(n+3)!) for 0 <= k <= n. - Emeric Deutsch, Apr 29 2004 EXAMPLE Triangle begins:      1,      1,  1,      3,  3,     1,     14,  14,    6,   1,     84,  84,   40,  10,   1,    594, 594,  300,  90,  15,  1,   4719, 4719, 2475, 825, 175, 21, 1, ... MAPLE T:=(n, k)->(2*n-k)!*(2*n-k+2)!*(k+3)!/(n-k)!/(n-k+1)!/k!/(n+2)!/(n+3)!: seq(seq(T(n, k), k=0..n), n=0..10); MATHEMATICA Flatten[Table[((2n-k)!(2n-k+2)!(k+3)!)/((n-k)!(n-k+1)!k!(n+2)!(n+3)!), {n, 0, 10}, {k, 0, n}]] (* Harvey P. Dale, Jan 27 2012 *) PROG (PARI) T(n, k) = (2*n-k)!*(2*n-k+2)!*(k+3)!/((n-k)!*(n-k+1)!*k!*(n+2)!*(n+3)!); matrix(8, 8, n, k, if (n>=k, T(n-1, k-1))) \\ Michel Marcus, Mar 05 2020 (MAGMA) /* As triangle */ [[Factorial(2*n - k) * Factorial(2*n - k + 2) * Factorial(k + 3) / (Factorial(n - k) * Factorial(n - k + 1) * Factorial(k) * Factorial(n + 2) * Factorial(n + 3)): k in [0..n]]: n in [0.. 10]]; // Vincenzo Librandi, Mar 06 2020 CROSSREFS Reflection of A039798. Sequence in context: A115193 A227343 A216294 * A143171 A112292 A001497 Adjacent sequences:  A039794 A039795 A039796 * A039798 A039799 A039800 KEYWORD nonn,tabl,easy,nice AUTHOR EXTENSIONS More terms from Emeric Deutsch, Apr 29 2004 STATUS approved

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Last modified December 8 08:31 EST 2021. Contains 349594 sequences. (Running on oeis4.)