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A158389
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A triangle of matrix polynomials: M(d)=Reverse[Table[If[ m <= n, m, 0], {n, 1, d}, {m, 1, d}]].
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0
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1, 1, -1, -2, -1, 1, -6, 3, 3, -1, 24, 8, -13, -3, 1, 120, -40, -61, 17, 6, -1, -720, -180, 360, 75, -45, -6, 1, -5040, 1260, 2368, -529, -309, 55, 10, -1, 40320, 8064, -18296, -3256, 2545, 363, -115, -10, 1, 362880, -72576, -155736, 28728, 21609, -3465
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Row sums are:
{1, 0, -2, -1, 17, 41, -515, -2186, 29616, 180497, -2730775,...}.
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FORMULA
| M(d)=Reverse[Table[If[ m <= n, m, 0], {n, 1, d}, {m, 1, d}]];
out_(n,m)=coefficients(characteristicpolynomial(M(n),x),x)
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EXAMPLE
| {1},
{1, -1},
{-2, -1, 1},
{-6, 3, 3, -1},
{24, 8, -13, -3, 1},
{120, -40, -61, 17, 6, -1},
{-720, -180, 360, 75, -45, -6, 1},
{-5040, 1260, 2368, -529, -309, 55, 10, -1},
{40320, 8064, -18296, -3256, 2545, 363, -115, -10, 1},
{ 362880, -72576, -155736, 28728, 21609, -3465, -1092, 135, 15, -1},
{-3628800, -604800, 1499160, 229700, -210946, -28077, 12001, 1246, -245, -15, 1}
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MATHEMATICA
| Clear[M, T, d, a, x, a0];
M[d_] := Reverse[Table[If[ m <= n, m, 0], {n, 1, d}, {m, 1, d}]];
a0 = Table[M[d], {d, 1, 10}];
Table[Det[M[d]], {d, 1, 10}];
Table[CharacteristicPolynomial[M[d], x], {d, 1, 10}];
Flatten[a]
Join[{1}, Table[Apply[Plus, CoefficientList[ Expand[CharacteristicPolynomial[M[n], x]], x]], {n, 1, 10}];
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CROSSREFS
| Sequence in context: A144351 A142589 A172400 * A186287 A186023 A103880
Adjacent sequences: A158386 A158387 A158388 * A158390 A158391 A158392
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KEYWORD
| sign,tabl
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Mar 17 2009
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