%I #12 Jul 31 2015 21:48:22
%S 0,4,33,129,355,795,1554,2758,4554,7110,10615,15279,21333,29029,38640,
%T 50460,64804,82008,102429,126445,154455,186879,224158,266754,315150,
%U 369850,431379,500283,577129,662505,757020,861304,976008,1101804,1239385,1389465
%N A008893/2.
%H Nathaniel Johnston, <a href="/A152041/b152041.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5, -10, 10, -5, 1).
%F a(n) = n*(n+1)*(7*n^2+7*n+2)/8.
%F G.f.: -x*(4*x^2+13*x+4)/(x-1)^5.
%F a(0)=0, a(1)=4, a(2)=33, a(3)=129, a(4)=355, a(n)=5*a(n-1)- 10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5) [From Harvey P. Dale, Jul 20 2011]
%t Table[n(n+1)(7n^2+7n+2)/8,{n,0,40}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{0,4,33,129,355},40] (* _Harvey P. Dale_, Jul 20 2011 *)
%o (Maxima) A152041(n):=n*(n+1)*(7*n^2+7*n+2)/8$
%o makelist(A152041(n),n,0,30); /* _Martin Ettl_, Nov 03 2012 */
%K nonn,easy
%O 0,2
%A M. F. Hasler, Sep 15 2009
%E Extended and edited by _Nathaniel Johnston_, May 05 2011