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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
1, 1, 1, 1, 6, 1, 1, 31, 31, 1, 1, 144, 648, 144, 1, 1, 625, 11292, 11292, 625, 1, 1, 2610, 184995, 751194, 184995, 2610, 1, 1, 10675, 2977413, 48401607, 48401607, 2977413, 10675, 1, 1, 43188, 47703610, 3101595936, 12443070892, 3101595936, 47703610 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
Row sums are:
{1, 2, 8, 64, 938, 23836, 1126406, 102779392, 18741756362, 6775770435604,
4926666872667614,...}.
LINKS
FORMULA
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))
EXAMPLE
{1},
{1, 1},
{1, 6, 1},
{1, 31, 31, 1},
{1, 144, 648, 144, 1},
{1, 625, 11292, 11292, 625, 1},
{1, 2610, 184995, 751194, 184995, 2610, 1},
{1, 10675, 2977413, 48401607, 48401607, 2977413, 10675, 1},
{1, 43188, 47703610, 3101595936, 12443070892, 3101595936, 47703610, 43188, 1},
{1, 173749, 763487338, 198555049906, 3188566506808, 3188566506808, 198555049906, 763487338, 173749, 1},
{1, 697014, 12216584973, 12708313657962, 816471906960456, 3268281996866802, 816471906960456, 12708313657962, 12216584973, 697014, 1}
MATHEMATICA
<< DiscreteMath`Combinatorica` ;
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]);
Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 2, 12}]
CROSSREFS
Sequence in context: A174186 A111578 A166349 * A157155 A022169 A156601
KEYWORD
nonn,tabl,uned
AUTHOR
Roger L. Bagula, Apr 17 2010
STATUS
approved

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Last modified June 14 23:20 EDT 2024. Contains 373401 sequences. (Running on oeis4.)