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 A176429 A symmetrical triangle sequence:q=4;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)) 0

%I

%S 1,1,1,1,6,1,1,31,31,1,1,144,648,144,1,1,625,11292,11292,625,1,1,2610,

%T 184995,751194,184995,2610,1,1,10675,2977413,48401607,48401607,

%U 2977413,10675,1,1,43188,47703610,3101595936,12443070892,3101595936,47703610

%N A symmetrical triangle sequence:q=4;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, 8, 64, 938, 23836, 1126406, 102779392, 18741756362, 6775770435604,

%C 4926666872667614,...}.

%F q=4;

%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, 6, 1},

%e {1, 31, 31, 1},

%e {1, 144, 648, 144, 1},

%e {1, 625, 11292, 11292, 625, 1},

%e {1, 2610, 184995, 751194, 184995, 2610, 1},

%e {1, 10675, 2977413, 48401607, 48401607, 2977413, 10675, 1},

%e {1, 43188, 47703610, 3101595936, 12443070892, 3101595936, 47703610, 43188, 1},

%e {1, 173749, 763487338, 198555049906, 3188566506808, 3188566506808, 198555049906, 763487338, 173749, 1},

%e {1, 697014, 12216584973, 12708313657962, 816471906960456, 3268281996866802, 816471906960456, 12708313657962, 12216584973, 697014, 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

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Last modified August 24 03:51 EDT 2019. Contains 326260 sequences. (Running on oeis4.)