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a(n) = ((n + 1)^2 * (5*n + 4)*n) / 12.
3

%I #9 Dec 10 2023 16:58:22

%S 0,3,21,76,200,435,833,1456,2376,3675,5445,7788,10816,14651,19425,

%T 25280,32368,40851,50901,62700,76440,92323,110561,131376,155000,

%U 181675,211653,245196,282576,324075,369985,420608,476256,537251

%N a(n) = ((n + 1)^2 * (5*n + 4)*n) / 12.

%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) = Sum_{k=0..n} A368045(k).

%F G.f.: x*(3 + 6*x + x^2)/(1 - x)^5. - _Stefano Spezia_, Dec 10 2023

%t A368046[n_]:=((n+1)^2(5n+4)n)/12;Array[A368046,50,0] (* or *)

%t LinearRecurrence[{5,-10,10,-5,1},{0,3,21,76,200},50] (* _Paolo Xausa_, Dec 10 2023 *)

%Y Cf. A368045.

%K nonn,easy

%O 0,2

%A _Peter Luschny_, Dec 09 2023