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 A264851 #15 Feb 16 2025 08:33:27
%S A264851 0,1,20,90,260,595,1176,2100,3480,5445,8140,11726,16380,22295,29680,
%T A264851 38760,49776,62985,78660,97090,118580,143451,172040,204700,241800,
%U A264851 283725,330876,383670,442540,507935,580320,660176,748000,844305,949620,1064490,1189476
%N A264851 a(n) = n*(n + 1)*(n + 2)*(4*n - 3)/6.
%C A264851 Partial sums of 18-gonal (or octadecagonal) pyramidal numbers. Therefore, this is the case k=8 of the general formula n*(n + 1)*(n + 2)*(k*n - k + 2)/12, which is related to 2*(k+1)-gonal pyramidal numbers.
%H A264851 OEIS Wiki, <a href="https://oeis.org/wiki/Figurate_numbers">Figurate numbers</a>
%H A264851 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PyramidalNumber.html">Pyramidal Number</a>
%H A264851 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A264851 G.f.: x*(1 + 15*x)/(1 - x)^5.
%F A264851 a(n) = Sum_{k = 0..n} A172078(k).
%F A264851 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - _Vincenzo Librandi_, Nov 27 2015
%t A264851 Table[n (n + 1) (n + 2) (4 n - 3)/6, {n, 0, 50}]
%o A264851 (Magma) [n*(n + 1)*(n + 2)*(4*n - 3)/6: n in [0..50]]; // _Vincenzo Librandi_, Nov 27 2015
%o A264851 (PARI) a(n)=n*(n+1)*(n+2)*(4*n-3)/6 \\ _Charles R Greathouse IV_, Jul 26 2016
%Y A264851 Cf. A172078.
%Y A264851 Cf. similar sequences with formula n*(n+1)*(n+2)*(k*n-k+2)/12 listed in A264850.
%K A264851 nonn,easy
%O A264851 0,3
%A A264851 _Ilya Gutkovskiy_, Nov 26 2015