A080275 a(n)=(-1)^n(1 - (1/12)n(n + 1)(12 - n + n^2)).

1, 1, -6, 17, -39, 79, -146, 251, -407, 629, -934, 1341, -1871, 2547, -3394, 4439, -5711, 7241, -9062, 11209, -13719, 16631, -19986, 23827, -28199, 33149, -38726, 44981, -51967, 59739, -68354, 77871, -88351, 99857, -112454, 126209, -141191, 157471, -175122, 194219, -214839, 237061, -260966

Offset

0,3

Comments

a(n) is the determinant of the n X n matrix M with M(i,i)=2i-1, M(i,j)=i+j.

Links

Table of n, a(n) for n=0..42.

Index entries for linear recurrences with constant coefficients, signature (-5,-10,-10,-5,-1).

Formula

G.f.: (1 + 6x + 9x^2 + 7x^3 + x^4)/(1 + x)^5.

a(n) = (-1)^n * (1 - A002378(n) - A002415(n)).

Mathematica

CoefficientList[Series[(1 + 6x + 9x^2 + 7x^3 + x^4)/(1 + x)^5, {x, 0, 50}], x]
LinearRecurrence[{-5, -10, -10, -5, -1}, {1, 1, -6, 17, -39}, 50] (* Harvey P. Dale, Jun 16 2023 *)

Crossrefs

Cf. A002378, A002415.

Sequence in context: A004799 A085278 A366104 * A061349 A213780 A101945

Adjacent sequences: A080272 A080273 A080274 * A080276 A080277 A080278

Keyword

easy,sign

Author

Mario Catalani (mario.catalani(AT)unito.it), Feb 12 2003

Status

approved