A174791 A symmetrical triangular sequence:t(n,m)=(n!^2/(m!(n - m)!))*Eulerian[n + 1, m] - (n!^2/(m!(n - m)!)) + 1

1, 1, 1, 1, 13, 1, 1, 181, 181, 1, 1, 2401, 9361, 2401, 1, 1, 33601, 361201, 361201, 33601, 1, 1, 514081, 12852001, 34776001, 12852001, 514081, 1, 1, 8678881, 454265281, 2755015201, 2755015201, 454265281, 8678881, 1, 1, 161602561

Offset

0,5

Comments

Row sums are:

{1, 2, 15, 364, 14165, 789606, 61508167, 6435918728, 872578586889,

148832934243850, 31190016903091211,...}.

Links

Table of n, a(n) for n=0..37.

Formula

t(n,m)=(n!^2/(m!(n - m)!))*Eulerian[n + 1, m] - (n!^2/(m!(n - m)!)) + 1

Example

{1},
{1, 1},
{1, 13, 1},
{1, 181, 181, 1},
{1, 2401, 9361, 2401, 1},
{1, 33601, 361201, 361201, 33601, 1},
{1, 514081, 12852001, 34776001, 12852001, 514081, 1},
{1, 8678881, 454265281, 2755015201, 2755015201, 454265281, 8678881, 1},
{1, 161602561, 16490718721, 199223055361, 440827833601, 199223055361, 16490718721, 161602561, 1}, {1, 3305111041, 624953387521, 13875095646721, 59913112976641, 59913112976641, 13875095646721, 624953387521, 3305111041, 1}, {1, 73846080001, 24924848256001, 959521635072001, 7420909535424001, 14379157173427201, 7420909535424001, 959521635072001, 24924848256001, 73846080001, 1}

Mathematica

<< DiscreteMath`Combinatorica`
t[n_, m_] = (n!^2/(m!(n - m)!))*Eulerian[n + 1, m] - (n!^2/(m!(n - m)!)) + 1
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]
Flatten[%]

Crossrefs

Sequence in context: A172300 A022176 A188646 * A015132 A066036 A010231

Adjacent sequences: A174788 A174789 A174790 * A174792 A174793 A174794

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Mar 29 2010

Status

approved