This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A257055 #14 Sep 08 2022 08:46:12
%S A257055 0,1,5,18,50,115,231,420,708,1125,1705,2486,3510,4823,6475,8520,11016,
%T A257055 14025,17613,21850,26810,32571,39215,46828,55500,65325,76401,88830,
%U A257055 102718,118175,135315,154256,175120,198033,223125,250530,280386,312835,348023,386100
%N A257055 a(n) = n*(n + 1)*(n^2 - n + 3)/6.
%C A257055 Partial sums of A037235.
%C A257055 After 0, this sequence is the 2nd diagonal of the square array in A080851.
%C A257055 For n > 2, a(n)-n is the 4th column of the triangular array in A208657.
%H A257055 Bruno Berselli, <a href="/A257055/b257055.txt">Table of n, a(n) for n = 0..1000</a>
%H A257055 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A257055 G.f.: x*(1 + 3*x^2)/(1 - x)^5.
%F A257055 a(n) = 3*A000332(n+1) + A000332(n+3).
%F A257055 a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - _Wesley Ivan Hurt_, May 27 2021
%t A257055 Table[n (n + 1) (n^2 - n + 3)/6, {n, 40}]
%o A257055 (PARI) vector(40, n, n--; n*(n+1)*(n^2-n+3)/6)
%o A257055 (Magma) [n*(n+1)*(n^2-n+3)/6: n in [0..40]];
%o A257055 (Sage) [n*(n+1)*(n^2-n+3)/6 for n in (0..40)]
%Y A257055 Cf. A000332, A037235, A080851, A208657.
%Y A257055 Cf. similar sequences listed in A256859.
%K A257055 nonn,easy
%O A257055 0,3
%A A257055 _Bruno Berselli_, Apr 15 2015