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 A172373 Triangle T(n,k) read by rows: T(n, k) = A010048(n, k)*A010048(n, k-1)/n. 0
 1, 1, 1, 1, 2, 1, 1, 6, 6, 1, 1, 15, 45, 15, 1, 1, 40, 300, 300, 40, 1, 1, 104, 2080, 5200, 2080, 104, 1, 1, 273, 14196, 94640, 94640, 14196, 273, 1, 1, 714, 97461, 1689324, 4504864, 1689324, 97461, 714, 1, 1, 1870, 667590, 30375345, 210602392, 210602392 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS These numbers are called the FiboNarayana numbers by Garrett and Killpatrick. - Michel Marcus, Oct 23 2019 LINKS Kristina Garrett, Kendra Killpatrick, A Recursion for the FiboNarayana and the Generalized Narayana Numbers, arXiv:1910.08855 [math.CO], 2019. FORMULA T(n, k) = A010048(n, k) * A010048(n, k-1) / n where A010048 are the Fibonomial coefficients. - Michel Marcus, Oct 23 2019 EXAMPLE {1}, {1, 1}, {1, 2, 1}, {1, 6, 6, 1}, {1, 15, 45, 15, 1}, {1, 40, 300, 300, 40, 1}, {1, 104, 2080, 5200, 2080, 104, 1}, {1, 273, 14196, 94640, 94640, 14196, 273, 1}, {1, 714, 97461, 1689324, 4504864, 1689324, 97461, 714, 1}, {1, 1870, 667590, 30375345, 210602392, 210602392, 30375345, 667590, 1870, 1} PROG (PARI) fibonomial(n, k) = prod(j=0, k-1, fibonacci(n-j))/prod(j=1, k, fibonacci(j)); \\ A010048 T(n, k) = fibonomial(n, k)*fibonomial(n, k-1)/fibonacci(n); matrix(10, 10, n, k, T(n, k)) \\ to see the triangle \\ Michel Marcus, Oct 23 2019 CROSSREFS Cf. A010048 (Fibonomial coefficients), A001263 (Narayana numbers). Sequence in context: A223257 A173881 A329228 * A174411 A322620 A155795 Adjacent sequences:  A172370 A172371 A172372 * A172374 A172375 A172376 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Feb 01 2010 EXTENSIONS Edited by Michel Marcus and Joerg Arndt, Oct 23 2019 STATUS approved

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Last modified February 25 22:55 EST 2020. Contains 332270 sequences. (Running on oeis4.)