A156186 Triangle: m=3; e(n,k,n) = (k + m - 1)*e(n - 1, k, m) + (m*n - k + 1 - m)*e(n - 1, k - 1, m); t(n,k) = e(n,k,m) + e(n,n-k,m).

2, 1, 1, 1, 6, 1, 1, 30, 30, 1, 1, 159, 360, 159, 1, 1, 1119, 3639, 3639, 1119, 1, 1, 10932, 41262, 57414, 41262, 10932, 1, 1, 136764, 582642, 898632, 898632, 582642, 136764, 1, 1, 2031933, 9957168, 16634718, 17182152, 16634718, 9957168, 2031933, 1, 1

Offset: 0

Author

Roger L. Bagula, Feb 05 2009

Keywords

• nonn
• tabl
• less
• uned

Examples

			{2},
{1, 1},
{1, 6, 1},
{1, 30, 30, 1},
{1, 159, 360, 159, 1},
{1, 1119, 3639, 3639, 1119, 1},
{1, 10932, 41262, 57414, 41262, 10932, 1},
{1, 136764, 582642, 898632, 898632, 582642, 136764, 1},
{1, 2031933, 9957168, 16634718, 17182152, 16634718, 9957168, 2031933, 1},...
		

Crossrefs

Cf. A054091, A054090, A008517, A156141.

Programs

Mathematica

m = 3; e[n_, 0, m_] := 1;
e[n_, k_, m_] := 0 /; k >= n;
e[n_, k_, 1] := 1 /; k >= n;
e[n_, k_, m_] := (k + m - 1)e[n - 1, k, m] + (m*n - k + 1 - m)e[n - 1, k - 1, m];
Table[Table[e[n, k, m], {k, 0, n - 1}], {n, 1, 10}];
Table[Table[e[n, k, m] + e[n, n - k, m], {k, 0, n}], {n, 0, 10}];
Flatten[%]

Formula

m=3; e(n,k,n) = (k + m - 1)*e(n - 1, k, m) + (m*n - k + 1 - m)*e(n - 1, k - 1, m);

t(n,k) = e(n,k,m) + e(n,n-k,m).