A076758 a(n) = n*(n+1)^2*(2+n)*(3+2*n)*(19+8*n)/180.

0, 9, 98, 516, 1870, 5369, 13132, 28560, 56772, 105105, 183678, 306020, 489762, 757393, 1137080, 1663552, 2379048, 3334329, 4589754, 6216420, 8297366, 10928841, 14221636, 18302480, 23315500, 29423745, 36810774, 45682308, 56267946, 68822945, 83630064

Offset

0,2

Comments

Let M_n be the n X n matrix M_(i,j) = i^2-j^2. Then the characteristic polynomial of M_n is x^n+a(n-1)x^(n-2). - Benoit Cloitre, Nov 30 2002

Links

Table of n, a(n) for n=0..30.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

G.f.: -x*(x^3+19*x^2+35*x+9)/(x-1)^7. [Colin Barker, Oct 22 2012]

a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7). - Wesley Ivan Hurt, May 24 2021

Mathematica

Table[n (n+1)^2(2+n)(3+2n)(19+8n)/180, {n, 0, 30}] (* or *) LinearRecurrence[ {7, -21, 35, -35, 21, -7, 1}, {0, 9, 98, 516, 1870, 5369, 13132}, 40] (* Harvey P. Dale, Dec 19 2017 *)

Crossrefs

Sequence in context: A123821 A145509 A098782 * A085868 A147637 A057933

Adjacent sequences: A076755 A076756 A076757 * A076759 A076760 A076761

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 14 2002

Status

approved