OFFSET
1,2
COMMENTS
See Novelli-Thibon (2014) for precise definition.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..11325
Paul Barry, On the inversion of Riordan arrays, arXiv:2101.06713 [math.CO], 2021.
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-François Alcover, Feb 12 2019 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Jun 13 2014
EXTENSIONS
More terms from Werner Schulte, Nov 22 2018
STATUS
approved