A174966 - OEIS

%I #2 Mar 30 2012 17:34:40

%S 1,1,1,1,-2,1,1,-19,-19,1,1,-74,-324,-74,1,1,-223,-2708,-2708,-223,1,

%T 1,-594,-16659,-45884,-16659,-594,1,1,-1475,-85839,-531011,-531011,

%U -85839,-1475,1,1,-3506,-394388,-4852814,-10777040,-4852814,-394388,-3506,1,1

%N A symmetrical triangle sequence: q=1;t(n,m,q)=If[q == 1, Binomial[n, m] + Eulerian[n + 1, m] - Binomial[n, m]*Eulerian[n + 1, m], (q - 1) + Binomial[n, m]^q + Eulerian[n + 1, m]^q - q*Binomial[n, m]*Eulerian[n + 1, m]]

%C Row sums are:

%C {1, 2, 0, -36, -470, -5860, -80388, -1236648, -21278454, -406514868,

%C -8555215724,...}.

%F q=1;

%F t(n,m,q)=If[q == 1, Binomial[n, m] + Eulerian[n + 1, m] - Binomial[n, m]*Eulerian[n + 1, m], (q - 1) + Binomial[n, m]^q + Eulerian[n + 1, m]^q - q*Binomial[n, m]*Eulerian[n + 1, m]]

%e {1},

%e {1, 1},

%e {1, -2, 1},

%e {1, -19, -19, 1},

%e {1, -74, -324, -74, 1},

%e {1, -223, -2708, -2708, -223, 1},

%e {1, -594, -16659, -45884, -16659, -594, 1},

%e {1, -1475, -85839, -531011, -531011, -85839, -1475, 1},

%e {1, -3506, -394388, -4852814, -10777040, -4852814, -394388, -3506, 1},

%e {1, -8095, -1674364, -37780852, -163794124, -163794124, -37780852, -1674364, -8095, 1},

%e {1, -18314, -6715983, -262214952, -2035265616, -3946785996, -2035265616, -262214952, -6715983, -18314, 1}

%t << DiscreteMath`Combinatorica`

%t t[n_, m_, q_] = If[q == 1, Binomial[n, m] + Eulerian[n + 1, m] - Binomial[n, m]*Eulerian[n + 1, m], (q - 1) + Binomial[ n, m]^q + Eulerian[n + 1, m]^q - q*Binomial[n, m]*Eulerian[n + 1, m]];

%t Table[Table[Sum[t[n, m, q], {m, 0, n}], {n, 0, 10}], {q, 1, 10}]

%Y Cf. A174912, A174914

%K sign,tabl,uned

%O 0,5

%A _Roger L. Bagula_, Apr 02 2010