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A156612
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A q-factorial triangle sequence built of Cartan D_n polynomials as anti-diagonals: p(x,n)=CartanDn(x,n): t(n,k)=If[m == 0, n!, Product[p(m+1),k), {k, 1, n}]];
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1, 1, 1, 1, 1, 2, 1, 1, 0, 6, 1, 1, -1, 0, 24, 1, 1, -2, -1, 0, 120, 1, 1, -3, -8, -1, 0, 720, 1, 1, -4, -27, 32, 2, 0, 5040, 1, 1, -5, -64, 567, 128, 2, 0, 40320, 1, 1, -6, -125, 3584, 30618, -512, 2, 0, 362880, 1, 1, -7, -216, 14375, 745472, -4317138, -2048, -4, 0, 3628800
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| Row sums are:
{1, 2, 4, 8, 25, 119, 710, 5045, 40950, 396443, 69236,...}.
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FORMULA
| p(x,n)=CartanDn(x,n):
t(n,k)=If[m == 0, n!, Product[p(m+1),k), {k, 1, n}]];
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EXAMPLE
| {1},
{1, 1},
{1, 1, 2},
{1, 1, 0, 6},
{1, 1, -1, 0, 24},
{1, 1, -2, -1, 0, 120},
{1, 1, -3, -8, -1, 0, 720},
{1, 1, -4, -27, 32, 2, 0, 5040},
{1, 1, -5, -64, 567, 128, 2, 0, 40320},
{1, 1, -6, -125, 3584, 30618, -512, 2, 0, 362880},
{1, 1, -7, -216, 14375, 745472, -4317138, -2048, -4, 0, 3628800}
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MATHEMATICA
| Clear[t, n, m, i, k, a, b];
T[n_, m_, d_] := If[ n == m, 2, If[(m == d && n == d - 2) || (n == d && m == d - 2), -1, If[(n == m - 1 || n == m + 1) && n <= d - 1 && m <= d - 1, -1, 0]]];
M[d_] := Table[T[n, m, d], {n, 1, d}, {m, 1, d}];
p[x_, n_] := If[n == 0, 1, CharacteristicPolynomial[M[n], x]];
a0 = Table[p[x, n], {n, 0, 20}] /. x -> m + 1;
t[n_, m_] = If[m == 0, n!, Product[a0[[k]], {k, 1, n}]];
a = Table[Table[t[n, m], {n, 0, 10}], {m, 0, 10}];
b = Table[Table[a[[m, n - m + 1]], {m, n, 1, -1}], {n, 1, Length[a]}];
Flatten[%]
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CROSSREFS
| Sequence in context: A064879 A173591 A156603 * A096801 A072407 A061158
Adjacent sequences: A156609 A156610 A156611 * A156613 A156614 A156615
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KEYWORD
| sign,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 11 2009
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