%I #23 Sep 08 2022 08:46:25

%S 0,4,19,56,130,260,469,784,1236,1860,2695,3784,5174,6916,9065,11680,

%T 14824,18564,22971,28120,34090,40964,48829,57776,67900,79300,92079,

%U 106344,122206,139780,159185,180544,203984,229636,257635,288120,321234,357124,395941,437840

%N a(n) = (n^4 + 5*n^3 + 11*n^2 + 7*n)/6.

%H Harvey P. Dale, <a href="/A332697/b332697.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 Row sums of A332023.

%F G.f.: x*(x^2 - x + 4)/(1 - x)^5. - _Petros Hadjicostas_, Jul 26 2020

%p a := n ->(5*n^3 + 11*n^2 + 7*n + n^4)/6: seq(a(n), n=0..50);

%t Table[(n^4+5n^3+11n^2+7n)/6,{n,0,40}] (* or *) LinearRecurrence[{5,-10,10,-5,1},{0,4,19,56,130},40] (* _Harvey P. Dale_, Apr 09 2022 *)

%o (Magma) [(5*n^3 + 11*n^2 + 7*n + n^4)/6 : n in [0..50]]; // _Wesley Ivan Hurt_, Jul 26 2020

%Y Cf. A332023.

%Y Column k = 4 of A128134 (shifted).

%K nonn,easy

%O 0,2

%A _Peter Luschny_, Feb 20 2020