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%I #17 Apr 30 2016 18:39:15
%S 0,0,4,64,400,1600,4900,12544,28224,57600,108900,193600,327184,529984,
%T 828100,1254400,1849600,2663424,3755844,5198400,7075600,9486400,
%U 12545764,16386304,21160000,27040000,34222500,42928704,53406864,65934400,80820100,98406400
%N 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).
%C Created in an attempt to repair a formula in A045996, which however turned out to be correct after all.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F 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
%F G.f.: 4*x^2*(1+x)*(x^2+8*x+1)/(1-x)^7. - _R. J. Mathar_, May 23 2010
%t 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 *)
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, May 19 2010, May 22 2010