A158389 Triangle of characteristic polynomials, see Mathematica code.

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

Offset

0,4

Links

Table of n, a(n) for n=0..54.

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

Triangle begins:
  {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

M[d_] := Reverse[Table[If[ m <= n, m, 0], {n, 1, d}, {m, 1, d}]];
a = Table[CharacteristicPolynomial[M[d], x], {d, 1, 10}];
Join[{1}, Flatten[CoefficientList[a, x]]]

Crossrefs

Sequence in context: A172400 A380401 A226691 * A186287 A318393 A340128

Adjacent sequences: A158386 A158387 A158388 * A158390 A158391 A158392

Keyword

sign,tabl,less

Author

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

Status

approved