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A158389 A triangle of matrix polynomials: M(d)=Reverse[Table[If[ m <= n, m, 0], {n, 1, d}, {m, 1, d}]]. 0
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; text; internal format)
OFFSET

0,4

COMMENTS

Row sums are:

{1, 0, -2, -1, 17, 41, -515, -2186, 29616, 180497, -2730775,...}.

LINKS

Table of n, a(n) for n=0..50.

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)

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}

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}];

CROSSREFS

Sequence in context: A284308 A172400 A226691 * A186287 A318393 A139622

Adjacent sequences:  A158386 A158387 A158388 * A158390 A158391 A158392

KEYWORD

sign,tabl

AUTHOR

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

STATUS

approved

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Last modified April 5 17:03 EDT 2020. Contains 333245 sequences. (Running on oeis4.)