A176427 - OEIS

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

%S 1,1,1,1,2,1,1,3,3,1,1,4,4,4,1,1,5,8,8,5,1,1,6,111,374,111,6,1,1,7,

%T 1041,8003,8003,1041,7,1,1,8,6982,106076,245384,106076,6982,8,1,1,9,

%U 39030,1120878,5309140,5309140,1120878,39030,9,1,1,10,195865,10491942

%N A symmetrical triangle sequence:q=2;c(n,q)=Product[1 - q^i, {i, 1, n}];t(n,m,q)=-Eulerian[n + 1, m] + 2*c(n, q)/(c(m, q)*c(n - m, q))

%C Row sums are:

%C {1, 2, 4, 8, 14, 28, 610, 18104, 471518, 12938116, 419594410,...}.

%F q=2;

%F c(n,q)=Product[1 - q^i, {i, 1, n}];

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

%e {1},

%e {1, 1},

%e {1, 2, 1},

%e {1, 3, 3, 1},

%e {1, 4, 4, 4, 1},

%e {1, 5, 8, 8, 5, 1},

%e {1, 6, 111, 374, 111, 6, 1},

%e {1, 7, 1041, 8003, 8003, 1041, 7, 1},

%e {1, 8, 6982, 106076, 245384, 106076, 6982, 8, 1},

%e {1, 9, 39030, 1120878, 5309140, 5309140, 1120878, 39030, 9, 1},

%e {1, 10, 195865, 10491942, 97749860, 202719054, 97749860, 10491942, 195865, 10, 1}

%t << DiscreteMath`Combinatorica` ;

%t c[n_, q_] = Product[1 - q^i, {i, 1, n}];

%t t[n_, m_, q_] = -Eulerian[n + 1, m] + 2*c[n, q]/(c[m, q]*c[n - m, q]);

%t Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 2, 12}]

%K nonn,tabl,uned

%O 0,5

%A _Roger L. Bagula_, Apr 17 2010