%I #18 Sep 10 2022 07:35:14
%S 0,1,27,256,1325,4815,13916,34272,75006,149925,278905,489456,818467,
%T 1314131,2038050,3067520,4497996,6445737,9050631,12479200,16927785,
%U 22625911,29839832,38876256,50086250,63869325,80677701,101020752,125469631,154662075,189307390
%N a(n) = n*(n+1)^2*(6*n^3-5*n^2+3*n+2)/24.
%D T. A. Gulliver, Sequences from Cubes of Integers, Int. Math. Journal, 4 (2003), 439-445.
%H Vincenzo Librandi, <a href="/A101379/b101379.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F G.f.: x*(1 + 20*x + 88*x^2 + 65*x^3 + 6*x^4)/(1 - x)^7. - _Ilya Gutkovskiy_, Feb 24 2017
%F E.g.f.: exp(x)*x*(24 + 300*x + 712*x^2 + 459*x^3 + 97*x^4 + 6*x^5)/24. - _Stefano Spezia_, Sep 10 2022
%t Table[(n (1+n)^2 (2+n (3+n (-5+6 n))))/24,{n,0,40}] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,1,27,256,1325,4815,13916},40] (* _Harvey P. Dale_, Jun 20 2021 *)
%o (Magma) [n*(n+1)^2*(6*n^3-5*n^2+3*n+2)/24: n in [0..40]]; // _Vincenzo Librandi_, Jun 15 2011
%o (PARI) a(n)=n*(n+1)^2*(6*n^3-5*n^2+3*n+2)/24 \\ _Charles R Greathouse IV_, Feb 24 2017
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Jan 15 2005