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A158391 A triangle of matrix polynomials:( dot version) M(d)=Reverse[Table[If[ m <= n, m, 0], {n, 1, d}, {m, 1, d}]].Transpose[Reverse[Table[If[ m <= n, m, 0], {n, 1, d}, {m, 1, d}]]]. 0
1, 1, -1, 4, -6, 1, 36, -62, 20, -1, 576, -1064, 440, -50, 1, 14400, -27752, 13092, -2068, 105, -1, 518400, -1027872, 526240, -99568, 7476, -196, 1, 25401600, -51402528, 27827104, -5903560, 552368, -22488, 336, -1, 1625702400 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Row sums are:

{1, 0, -1, -7, -97, -2224, -75519, -3547169, -219848959, -17364520592,

-1701503169057,...}.

Example matrix:

M(3)={{14, 5, 1},

{5, 5, 1},

{1, 1, 1}}

LINKS

Table of n, a(n) for n=0..36.

FORMULA

M(d)=Reverse[Table[If[ m <= n, m, 0], {n, 1, d}, {m, 1, d}]].Transpose[Reverse[Table[If[ m <= n, m, 0], {n, 1, d}, {m, 1, d}]]];

out_(n,m)=coefficients(characteristicpolynomial(M(n),x),x)

EXAMPLE

{1},

{1, -1},

{4, -6, 1},

{36, -62, 20, -1},

{576, -1064, 440, -50, 1},

{14400, -27752, 13092, -2068, 105, -1},

{518400, -1027872, 526240, -99568, 7476, -196, 1},

{25401600, -51402528, 27827104, -5903560, 552368, -22488, 336, -1},

{1625702400, -3340564992, 1883221312, -432454176, 46632432, -2444400, 59004, -540, 1},

{131681894400, -273837169152, 159196654656, -38743828352, 4614308240, -285357704, 9115756, -139260, 825, -1},

{13168189440000, -27647080704000, 16465714101504, -4189435579520, 537035259392, -37331932704, 1435658576, -29713112, 302016, -1210, 1}

MATHEMATICA

Clear[M, T, d, a, x, a0];

M[d_] :=Reverse[Table[If[ m <= n, m, 0], {n, 1, d}, {m, 1, d}]].Transpose[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}];

CROSSREFS

Sequence in context: A230256 A193293 A258220 * A016491 A160327 A124259

Adjacent sequences:  A158388 A158389 A158390 * A158392 A158393 A158394

KEYWORD

sign,tabl

AUTHOR

Roger L. Bagula and Gary W. Adamson, Mar 17 2009

STATUS

approved

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Last modified February 21 03:02 EST 2020. Contains 332086 sequences. (Running on oeis4.)