%I #9 Jun 13 2015 00:52:34
%S 0,0,15,75,222,510,1005,1785,2940,4572,6795,9735,13530,18330,24297,
%T 31605,40440,51000,63495,78147,95190,114870,137445,163185,192372,
%U 225300,262275,303615,349650,400722,457185,519405,587760,662640,744447,833595,930510
%N (n^4 - 10*n^2 + 15*n - 6)/2.
%H Ellingsrud, Geir and Stromme, Stein Arild, <a href="http://arxiv.org/abs/alg-geom/9411005">Bott's formula and enumerative geometry</a>, J. Amer. Math. Soc. 9 (1996), 175-193. [arXiv:alg-geom/9411005]
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(1)=0, a(2)=0, a(3)=15, a(4)=75, a(5)=222, a(n)=5*a(n-1)-10*a(n-2)+ 10*a(n-3)- 5*a(n-4)+a(n-5). - _Harvey P. Dale_, Aug 12 2013
%F G.f.: 3*x^3*(-5+x^2) / (x-1)^5 . - _R. J. Mathar_, Apr 23 2015
%t Table[(n^4-10n^2+15n-6)/2,{n,40}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{0,0,15,75,222},40] (* _Harvey P. Dale_, Aug 12 2013 *)
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_, Mar 07 2008