0,1

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]

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).

{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}

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[%]

A157114, A157117

Sequence in context: A090628 A054387 A112734 this_sequence A156186 A156233 A060185

Adjacent sequences: A157115 A157116 A157117 this_sequence A157119 A157120 A157121

nonn,tabl,uned

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 23 2009