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A243663 Triangle read by rows: the reversed x = 1+q Narayana triangle at m=3. 1
1, 4, 1, 22, 11, 1, 140, 105, 21, 1, 969, 969, 306, 34, 1, 7084, 8855, 3850, 700, 50, 1, 53820, 80730, 44850, 11500, 1380, 69, 1, 420732, 736281, 498771, 166257, 28665, 2457, 91, 1, 3362260, 6724520, 5379616, 2215136, 503440, 62930, 4060, 116, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See Novelli-Thibon (2014) for precise definition.

LINKS

Table of n, a(n) for n=1..45.

J.-C. Novelli, J.-Y. Thibon, Hopf Algebras of m-permutations,(m+1)-ary trees, and m-parking functions, arXiv preprint arXiv:1403.5962, 2014. See Fig. 11.

FORMULA

T(n,k) = binomial(4*n+1-k,n-k) * binomial(n,k-1) / n for 1 <= k <= n, more generally: T_m(n,k) = binomial((m+1)*n+1-k,n-k) * binomial(n,k-1) / n for 1 <= k <= n and some fixed integer m > 1. - Werner Schulte, Nov 22 2018

EXAMPLE

Triangle begins:

     1

     4,    1

    22,   11,    1

   140,  105,   21,   1

   969,  969,  306,  34,  1

  7084, 8855, 3850, 700, 50, 1

  ...

MATHEMATICA

T[m_][n_, k_] := Binomial[(m + 1) n + 1 - k, n - k] Binomial[n, k - 1]/n;

Table[T[3][n, k], {n, 1, 9}, {k, 1, n}] // Flatten (* Jean-Fran├žois Alcover, Feb 12 2019 *)

CROSSREFS

Cf. A001263, A243662 (m=2).

Sequence in context: A299445 A135049 A113384 * A039812 A308559 A249268

Adjacent sequences:  A243660 A243661 A243662 * A243664 A243665 A243666

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Jun 13 2014

EXTENSIONS

More terms from Werner Schulte, Nov 22 2018

STATUS

approved

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Last modified July 12 10:09 EDT 2020. Contains 335657 sequences. (Running on oeis4.)