%I #17 Aug 04 2017 15:24:38
%S 0,10,42,108,220,390,630,952,1368,1890,2530,3300,4212,5278,6510,7920,
%T 9520,11322,13338,15580,18060,20790,23782,27048,30600,34450,38610,
%U 43092,47908,53070,58590,64480,70752,77418,84490,91980,99900,108262,117078,126360,136120
%N a(n) = n*(2*n^2 + 5*n + 3).
%H Vincenzo Librandi, <a href="/A163815/b163815.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F Row sums from A155151: a(n) = Sum_{m=1..n} 2*(2*m*n + m + n + 1).
%F a(n) = 2*A160378(n+1).
%F G.f.: 2*x*(5+x)/(x-1)^4.
%F a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4).
%F E.g.f.: (2*x^3 + 11*x^2 + 10*x)*exp(x). - _G. C. Greubel_, Aug 04 2017
%t CoefficientList[Series[2*x*(5+x)/(x-1)^4, {x, 0, 40}], x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 10, 42, 108}, 50](* _Vincenzo Librandi_, Mar 06 2012 *)
%o (PARI) x='x+O('x^50); concat([0], Vec(2*x*(5+x)/(x-1)^4)) \\ _G. C. Greubel_, Aug 04 2017
%Y Cf. A155151, A160378.
%K nonn,easy
%O 0,2
%A _Vincenzo Librandi_, Aug 04 2009
%E Edited and a(4) corrected by _R. J. Mathar_, Aug 05 2009