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%I #20 May 01 2021 21:32:51
%S 1,4,1,22,11,1,140,105,21,1,969,969,306,34,1,7084,8855,3850,700,50,1,
%T 53820,80730,44850,11500,1380,69,1,420732,736281,498771,166257,28665,
%U 2457,91,1,3362260,6724520,5379616,2215136,503440,62930,4060,116,1
%N Triangle read by rows: the reversed x = 1+q Narayana triangle at m=3.
%C See Novelli-Thibon (2014) for precise definition.
%H Michael De Vlieger, <a href="/A243663/b243663.txt">Table of n, a(n) for n = 1..11325</a>
%H Paul Barry, <a href="https://arxiv.org/abs/2101.06713">On the inversion of Riordan arrays</a>, arXiv:2101.06713 [math.CO], 2021.
%H J.-C. Novelli, J.-Y. Thibon, <a href="http://arxiv.org/abs/1403.5962">Hopf Algebras of m-permutations,(m+1)-ary trees, and m-parking functions</a>, arXiv preprint arXiv:1403.5962, 2014. See Fig. 11.
%F 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
%e Triangle begins:
%e 1
%e 4, 1
%e 22, 11, 1
%e 140, 105, 21, 1
%e 969, 969, 306, 34, 1
%e 7084, 8855, 3850, 700, 50, 1
%e ...
%t T[m_][n_, k_] := Binomial[(m + 1) n + 1 - k, n - k] Binomial[n, k - 1]/n;
%t Table[T[3][n, k], {n, 1, 9}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Feb 12 2019 *)
%Y Cf. A001263, A243662 (m=2).
%K nonn,tabl
%O 1,2
%A _N. J. A. Sloane_, Jun 13 2014
%E More terms from _Werner Schulte_, Nov 22 2018
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