%I #19 Dec 17 2019 05:26:34
%S 0,13,59,156,322,575,933,1414,2036,2817,3775,4928,6294,7891,9737,
%T 11850,14248,16949,19971,23332,27050,31143,35629,40526,45852,51625,
%U 57863,64584,71806,79547,87825,96658,106064,116061,126667,137900,149778
%N a(n) = n*(6*n^2 + 15*n + 5)/2.
%H Vincenzo Librandi, <a href="/A163833/b163833.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 A162245: a(n) = Sum_{m=1..n} (6*m*n + 3*m + 3*n + 1).
%F G.f.: x*(13 + 7*x - 2*x^2)/(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.: (1/2)*x*(26 + 33*x + 6*x^2)*exp(x). - _G. C. Greubel_, Aug 05 2017
%t CoefficientList[Series[-x*(-13-7*x+2*x^2)/(x-1)^4, {x, 0, 40}], x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 13, 59, 156}, 50](* _Vincenzo Librandi_, Mar 06 2012 *)
%o (PARI) x='x+O('x^50); concat([0], Vec(x*(13 +7*x -2*x^2)/(x-1)^4)) \\ _G. C. Greubel_, Aug 05 2017
%Y Cf. A162245.
%K nonn,easy
%O 0,2
%A _Vincenzo Librandi_, Aug 05 2009
%E Edited by _R. J. Mathar_, Aug 05 2009