login
a(n) = T(n^3) - T(n), where T() are the triangular numbers (A000217).
1

%I #12 Sep 08 2022 08:45:11

%S 0,0,33,372,2070,7860,23415,58968,131292,266040,500445,886380,1493778,

%T 2414412,3766035,5696880,8390520,12071088,17008857,23526180,32003790,

%U 42887460,56695023,74023752,95558100,122077800,154466325,193719708

%N a(n) = T(n^3) - T(n), where T() are the triangular numbers (A000217).

%H Vincenzo Librandi, <a href="/A085742/b085742.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = (n-1)*n*(n+1)*(n^3 + n + 1)/2.

%e a(3) = T(3^3) - T(3) = T(27) - T(3) = 378 - 6 = 372.

%o (PARI) t(n)=n*(n+1)/2; for(n=0,50,print1(t(n^3)-t(n)","))

%o (Magma) [(n-1)*n*(n+1)*(n^3+n+1)/2: n in [0..40]]; // _Vincenzo Librandi_, Sep 14 2011

%Y Cf. A000217.

%K nonn,easy

%O 0,3

%A _Jon Perry_, Jul 21 2003