A174791 - OEIS

%I #4 May 15 2013 18:48:00

%S 1,1,1,1,13,1,1,181,181,1,1,2401,9361,2401,1,1,33601,361201,361201,

%T 33601,1,1,514081,12852001,34776001,12852001,514081,1,1,8678881,

%U 454265281,2755015201,2755015201,454265281,8678881,1,1,161602561

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

%C Row sums are:

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

%C 148832934243850, 31190016903091211,...}.

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

%e {1},

%e {1, 1},

%e {1, 13, 1},

%e {1, 181, 181, 1},

%e {1, 2401, 9361, 2401, 1},

%e {1, 33601, 361201, 361201, 33601, 1},

%e {1, 514081, 12852001, 34776001, 12852001, 514081, 1},

%e {1, 8678881, 454265281, 2755015201, 2755015201, 454265281, 8678881, 1},

%e {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}

%t << DiscreteMath`Combinatorica`

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

%t Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]

%t Flatten[%]

%K nonn,tabl,uned

%O 0,5

%A _Roger L. Bagula_, Mar 29 2010