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

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

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: A369435 A172400 A226691 * A186287 A318393 A340128

Adjacent sequences: A158386 A158387 A158388 * A158390 A158391 A158392

Keyword

sign,tabl

Author

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

Status

approved