A176560 A symmetrical triangle recursion:q=5;t(n,m,0)=Binomial[n,m];t(n,m,1)=Narayana(n,m);t(n,m,2)=Eulerian(n+1,m);t(n,m,q)=t(n,m,g-2)+t(n,m,q-3).

1, 1, 1, 1, 6, 1, 1, 16, 16, 1, 1, 35, 85, 35, 1, 1, 71, 351, 351, 71, 1, 1, 140, 1295, 2590, 1295, 140, 1, 1, 274, 4488, 16108, 16108, 4488, 274, 1, 1, 537, 14943, 89409, 157953, 89409, 14943, 537, 1, 1, 1057, 48379, 457711, 1315645, 1315645, 457711, 48379

Offset: 0

Author

Roger L. Bagula, Apr 20 2010

Keywords

• nonn
• tabl
• uned

Comments

Row sums are:

{1, 2, 8, 34, 157, 846, 5462, 41742, 367733, 3645586, 39975575,...}.

Examples

			{1},
{1, 1},
{1, 6, 1},
{1, 16, 16, 1},
{1, 35, 85, 35, 1},
{1, 71, 351, 351, 71, 1},
{1, 140, 1295, 2590, 1295, 140, 1},
{1, 274, 4488, 16108, 16108, 4488, 274, 1},
{1, 537, 14943, 89409, 157953, 89409, 14943, 537, 1},
{1, 1057, 48379, 457711, 1315645, 1315645, 457711, 48379, 1057, 1},
{1, 2090, 153461, 2208437, 9751973, 15743651, 9751973, 2208437, 153461, 2090, 1}
		

Crossrefs

Cf. A007318, A001263, A008292, A176490

Programs

Mathematica

<< DiscreteMath`Combinatorica`
t[n_, m_, 0] := Binomial[n, m];
t[n_, m_, 1] := Binomial[n, m]*Binomial[n + 1, m]/(m + 1);
t[n_, m_, 2] := Eulerian[1 + n, m];
t[n_, m_, q_] := t[n, m, q] = t[n, m, q - 2] + t[n, m, q - 3] - 1;
Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 0, 10}]

Formula

q=5;

t(n,m,0)=Binomial[n,m];

t(n,m,1)=Narayana(n,m);

t(n,m,2)=Eulerian(n+1,m);

t(n,m,q)=t(n,m,g-2)+t(n,m,q-3)