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A157118
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A Narayana type Chebyshev triangle sequence: t0(n,m)=If[m <= n, Narayana(n*m, n - m), Narayana(n*(n - m), m)]; t(n,m)=t0(n,m)+t0(n,n-m).
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2, 1, 1, 1, 6, 1, 1, 27, 27, 1, 1, 88, 672, 88, 1, 1, 225, 9150, 9150, 225, 1, 1, 486, 98385, 395352, 98385, 486, 1, 1, 931, 1126951, 11748681, 11748681, 1126951, 931, 1, 1, 1632, 14600320, 402703120, 588593280, 402703120, 14600320, 1632, 1, 1, 2673
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Row sums are:
{2, 2, 8, 56, 850, 18752, 593096, 25753128, 1423203426, 97093460216,
8037509878112,...}.
This sequence show this Chebyshev like process is 2*n and not n^2.
Like in the Narayana pattern, the fractal is like the binomial and Eulerian but not the same:
a = Table[Table[t[n, m] + t[n, n - m], {m, 0, n}], {n, 0, 128}];
b = Table[If[m <= n, Mod[a[[n]][[m]], 2], 0], {m, 1, Length[a]}, { n, 1, Length[a]}];
ListDensityPlot[b, Mesh -> False, Frame -> False]
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FORMULA
| t0(n,m)=If[m <= n, Narayana(n*m, n - m), Narayana(n*(n - m), m)];
t(n,m)=t0(n,m)+t0(n,n-m).
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EXAMPLE
| {2},
{1, 1},
{1, 6, 1},
{1, 27, 27, 1},
{1, 88, 672, 88, 1},
{1, 225, 9150, 9150, 225, 1},
{1, 486, 98385, 395352, 98385, 486, 1},
{1, 931, 1126951, 11748681, 11748681, 1126951, 931, 1},
{1, 1632, 14600320, 402703120, 588593280, 402703120, 14600320, 1632, 1},
{1, 2673, 201755880, 16093941435, 32251030119, 32251030119, 16093941435, 201755880, 2673, 1},
{1, 4150, 2851594500, 669943264300, 2516444348505, 1659031455200, 2516444348505, 669943264300, 2851594500, 4150, 1}
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MATHEMATICA
| Clear[t, n, m, f, A];
f[n_] = Product[k + 1, {k, 0, n}];
A[n_, m_] = Binomial[n, m]*f[n]/(f[m]*f[n - m]);
t[n_, m_] = If[m <= n, A[n*m, n - m], A[n*(n - m), m]];
Table[Table[t[n, m] + t[n, n - m], {m, 0, n}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
| A157114, A157117
Sequence in context: A054387 A199958 A112734 * A156186 A156233 A060185
Adjacent sequences: A157115 A157116 A157117 * A157119 A157120 A157121
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KEYWORD
| nonn,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 23 2009
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