A140356 Triangle T(n,m) read by rows: m! if m <= floor(n/2), and (n-m)! otherwise.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 6, 2, 1, 1, 1, 1, 2, 6, 6, 2, 1, 1, 1, 1, 2, 6, 24, 6, 2, 1, 1, 1, 1, 2, 6, 24, 24, 6, 2, 1, 1, 1, 1, 2, 6, 24, 120, 24, 6, 2, 1, 1, 1, 1, 2, 6, 24, 120, 120, 24, 6, 2, 1, 1, 1, 1, 2, 6, 24, 120, 720, 120, 24, 6, 2, 1, 1, 1, 1, 2, 6, 24

Offset: 0

Author

Roger L. Bagula and Gary W. Adamson, May 30 2008

Keywords

• nonn
• easy
• tabl

Comments

Row sums: 1, 2, 3, 4, 6, 8, 14, 20, 44, 68, 188,... which is

2*A003422((n+1)/2) if n is odd, and A003422(n/2)+A003422(1+n/2) if n is even.

Examples

			1,
1, 1,
1, 1, 1,
1, 1, 1, 1,
1, 1, 2, 1, 1,
1, 1, 2, 2, 1, 1,
1, 1, 2, 6, 2, 1, 1,
1, 1, 2, 6, 6, 2, 1, 1,
1, 1, 2, 6, 24, 6, 2, 1,1,
1, 1, 2, 6, 24, 24, 6, 2, 1, 1,
1, 1, 2, 6, 24, 120, 24, 6, 2, 1, 1
		

Programs

Mathematica

g[n_, m_] := If[m <= Floor[n/2], m!, (n - m)! ]; w = Table[Table[g[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[w] Table[Apply[Plus, Table[g[n, m], {m, 0, n}]], {n, 0, 10}]

Formula

T(n,m) = A000142(m) if m<=[n/2], = A000142(n-m) if m>[n/2], 0<=m<=n.

Conjecture: limit_{n->infinity} sum_{m=0..n} ( 1/binomial(n,m) - T(n,m) ) = 0.

T(n,m) = T(n,n-m).

Extensions

Non-Ascii characters corrected, offset set to 0, reported Mma experiments removed - The Assoc. Editors of the OEIS, Oct 31 2009