A176561 A symmetrical triangle recursion:q=6;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, 7, 1, 1, 18, 18, 1, 1, 38, 90, 38, 1, 1, 75, 360, 360, 75, 1, 1, 145, 1309, 2609, 1309, 145, 1, 1, 280, 4508, 16142, 16142, 4508, 280, 1, 1, 544, 14970, 89464, 158022, 89464, 14970, 544, 1, 1, 1065, 48414, 457794, 1315770, 1315770, 457794, 48414

Offset: 0

Author

Roger L. Bagula, Apr 20 2010

Keywords

• nonn
• tabl
• uned

Comments

Row sums are:

{1, 2, 9, 38, 168, 872, 5519, 41862, 367980, 3646088, 39976588,...}.

Examples

			{1},
{1, 1},
{1, 7, 1},
{1, 18, 18, 1},
{1, 38, 90, 38, 1},
{1, 75, 360, 360, 75, 1},
{1, 145, 1309, 2609, 1309, 145, 1},
{1, 280, 4508, 16142, 16142, 4508, 280, 1},
{1, 544, 14970, 89464, 158022, 89464, 14970, 544, 1},
{1, 1065, 48414, 457794, 1315770, 1315770, 457794, 48414, 1065, 1},
{1, 2099, 153505, 2208556, 9752182, 15743902, 9752182, 2208556, 153505, 2099, 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=6;

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)