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 A156608 A q-combination triangle sequence built of Cartan D_n polynomials: m=2;q=3; p(x,n)=CartanDn(x,n). t(n,k)=If[m == 0, n!, Product[p(m+1),k), {k, 1, n}]]; b(n,k,m)=If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])]. 0
 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -2, 2, 2, -2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, -1, 2, 2, -1, 1, 1, 1, -2, 2, 2, -4, 2, 2, -2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, -1, 2, 2, -1, 2, 2, -1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,17 COMMENTS Row sums are: {1, 2, 1, 4, 3, 2, 10, 6, 2, 16, 9,...}. LINKS FORMULA m=2;q=3; p(x,n)=CartanDn(x,n); t(n,k)=If[m == 0, n!, Product[p(m+1),k), {k, 1, n}]]; b(n,k,m)=If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])]. EXAMPLE {1}, {1, 1}, {1, -1, 1}, {1, 1, 1, 1}, {1, 1, -1, 1, 1}, {1, -2, 2, 2, -2, 1}, {1, 1, 2, 2, 2, 1, 1}, {1, 1, -1, 2, 2, -1, 1, 1}, {1, -2, 2, 2, -4, 2, 2, -2, 1}, {1, 1, 2, 2, 2, 2, 2, 2, 1, 1}, {1, 1, -1, 2, 2, -1, 2, 2, -1, 1, 1} 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}]]; b[n_, k_, m_] = If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])]; Table[Flatten[Table[Table[b[n, k, m], {k, 0, n}], {n, 0, 10}]], {m, 0, 15}] CROSSREFS Sequence in context: A282542 A271518 A106825 * A323827 A275850 A112505 Adjacent sequences:  A156605 A156606 A156607 * A156609 A156610 A156611 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Feb 11 2009 STATUS approved

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Last modified June 24 16:51 EDT 2021. Contains 345417 sequences. (Running on oeis4.)