A156188 Triangle: m=5; 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, 10, 1, 1, 80, 80, 1, 1, 775, 1520, 775, 1, 1, 10915, 25945, 25945, 10915, 1, 1, 213720, 542910, 624670, 542910, 213720, 1, 1, 5245530, 14690640, 16408670, 16408670, 14690640, 5245530, 1, 1, 151534685, 479956020, 553630850, 464654480

Offset: 0

Author

Roger L. Bagula, Feb 05 2009

Keywords

• nonn
• tabl
• uned

Examples

			{2},
{1, 1},
{1, 10, 1},
{1, 80, 80, 1},
{1, 775, 1520, 775, 1},
{1, 10915, 25945, 25945, 10915, 1},
{1, 213720, 542910, 624670, 542910, 213720, 1},
{1, 5245530, 14690640, 16408670, 16408670, 14690640, 5245530, 1},...
		

Crossrefs

Cf. A054091, A054090, A008517, A156141.

Programs

Mathematica

m = 5; 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=5; 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).