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%I #44 Feb 12 2018 11:25:59
%S 0,1,14,69,216,525,1086,2009,3424,5481,8350,12221,17304,23829,32046,
%T 42225,54656,69649,87534,108661,133400,162141,195294,233289,276576,
%U 325625,380926,442989,512344,589541,675150,769761,873984,988449,1113806,1250725,1399896
%N a(n) = (5*n^2 + 1)*n^2 / 6.
%C Partial sums of A005902. - _Jonathan Vos Post_, Mar 14 2006
%H Muniru A Asiru, <a href="/A008354/b008354.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5, -10, 10, -5, 1).
%F From _R. J. Mathar_, Aug 10 2008: (Start)
%F O.g.f.: x*(1 + x)*(x^2 + 8*x + 1)/(1 - x)^5.
%F a(n) = n*A004068(n). (End)
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>4, a(0)=0, a(1)=1, a(2)=14, a(3)=69, a(4)=216. - _Harvey P. Dale_, Feb 12 2015
%p a:= n-> 5*n^4/6 + n^2/6: seq(a(n), n=0..45);
%t Table[n^2 (5 n^2 + 1)/6, {n, 0, 30}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 14, 69, 216}, 30] (* _Harvey P. Dale_, Feb 12 2015 *)
%o (GAP) List([0..30], n -> (5*n^2+1)*n^2/6); # _Muniru A Asiru_, Feb 12 2018
%Y Cf. A005901, A005902.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_ and _J. H. Conway_
%E Definition corrected by _R. J. Mathar_, Aug 10 2008
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