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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

Table of n, a(n) for n=1..51.

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.)