0,5

Row sums are:

{1, 2, -1, 20, 23, 866, -1126, 243542, 1299410, 516760688, -7620005169,...}.

m=4;q=5; 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])].

{1},

{1, 1},

{1, -3, 1},

{1, 9, 9, 1},

{1, -21, 63, -21, 1},

{1, 54, 378, 378, 54, 1},

{1, -141, 2538, -5922, 2538, -141, 1},

{1, 369, 17343, 104058, 104058, 17343, 369, 1},

{1, -966, 118818, -1861482, 4786668, -1861482, 118818, -966, 1},

{1, 2529, 814338, 33387858, 224175618, 224175618, 33387858, 814338, 2529, 1},

{1, -6621, 5581503, -599081322, 10526714658, -27486421607, 10526714658, -599081322, 5581503, -6621, 1}

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}]

Sequence in context: A144183 A050153 A106340 this_sequence A157179 A152655 A144493

Adjacent sequences: A156607 A156608 A156609 this_sequence A156611 A156612 A156613

sign,tabl,uned

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 11 2009