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A243663
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Triangle read by rows: the reversed x = 1+q Narayana triangle at m=3.
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2
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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
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OFFSET
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1,2
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COMMENTS
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See Novelli-Thibon (2014) for precise definition.
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LINKS
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FORMULA
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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
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EXAMPLE
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Triangle begins:
1
4, 1
22, 11, 1
140, 105, 21, 1
969, 969, 306, 34, 1
7084, 8855, 3850, 700, 50, 1
...
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MATHEMATICA
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T[m_][n_, k_] := Binomial[(m + 1) n + 1 - k, n - k] Binomial[n, k - 1]/n;
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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