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A156612 A q-factorial triangle sequence built of Cartan D_n polynomials as antidiagonals: p(x,n)=CartanDn(x,n): t(n,k)=If[m == 0, n!, Product[p(m+1),k), {k, 1, n}]]; 0
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; text; internal format)
OFFSET

0,6

COMMENTS

Row sums are:

{1, 2, 4, 8, 25, 119, 710, 5045, 40950, 396443, 69236,...}.

LINKS

Table of n, a(n) for n=0..65.

FORMULA

p(x,n)=CartanDn(x,n):

t(n,k)=If[m == 0, n!, Product[p(m+1),k), {k, 1, n}]];

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}

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[%]

CROSSREFS

Sequence in context: A173591 A343320 A156603 * A342645 A096801 A072407

Adjacent sequences:  A156609 A156610 A156611 * A156613 A156614 A156615

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Feb 11 2009

STATUS

approved

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Last modified May 17 22:15 EDT 2021. Contains 343992 sequences. (Running on oeis4.)