A169801 a(n) = ((n-1)^2*n^2*(n+1)^2)/6 - 2*Sum_{l=2..n}Sum_{k=2..n}(n-k+1)*(n-l+1)*(k-1)*(l-1).

0, 0, 4, 64, 400, 1600, 4900, 12544, 28224, 57600, 108900, 193600, 327184, 529984, 828100, 1254400, 1849600, 2663424, 3755844, 5198400, 7075600, 9486400, 12545764, 16386304, 21160000, 27040000, 34222500, 42928704, 53406864, 65934400, 80820100, 98406400

Offset: 0

Author

N. J. A. Sloane, May 19 2010, May 22 2010

Keywords

• nonn
• easy

Comments

Created in an attempt to repair a formula in A045996, which however turned out to be correct after all.

Links

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

Programs

Mathematica

f[n_] := ((n - 1)^2*n^2*(n + 1)^2)/6 - 2*Sum[(n - k + 1)*(n - l + 1)*(k - 1) (l - 1), {k, 2, n}, {l, 2, n}]; Array[f, 31] (* Robert G. Wilson v, May 23 2010 *)

Formula

a(n) = A099764(n-1) - 2*Sum_{l=2..n}Sum_{k=2..n}(n-k+1)*(n-l+1)*(k-1)*(l-1) = A099764(n-1)/9 = 4*A001249(n-2). - R. J. Mathar, May 23 2010

G.f.: 4*x^2*(1+x)*(x^2+8*x+1)/(1-x)^7. - R. J. Mathar, May 23 2010