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 A256647 #39 Aug 04 2025 11:24:57
%S A256647 0,1,28,106,260,515,896,1428,2136,3045,4180,5566,7228,9191,11480,
%T A256647 14120,17136,20553,24396,28690,33460,38731,44528,50876,57800,65325,
%U A256647 73476,82278,91756,101935,112840,124496,136928,150161,164220,179130,194916,211603,229216
%N A256647 27-gonal pyramidal numbers: a(n) = n*(n+1)*(25*n-22)/6.
%C A256647 See comments in A256645.
%D A256647 E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 93 (25th row of the table).
%H A256647 Luciano Ancora, <a href="/A256647/b256647.txt">Table of n, a(n) for n = 0..1000</a>
%H A256647 Luciano Ancora, <a href="/A256645/a256645_1.pdf">Polygonal and Pyramidal numbers</a>, Section 3.
%H A256647 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A256647 G.f.: x*(1 + 24*x)/(1 - x)^4.
%F A256647 a(n) = A000292(n) + 24*A000292(n-1).
%F A256647 From _Elmo R. Oliveira_, Aug 04 2025: (Start)
%F A256647 E.g.f.: exp(x)*x*(6 + 78*x + 25*x^2)/6.
%F A256647 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)
%t A256647 Table[n (n + 1) (25 n - 22)/6, {n, 0, 40}]
%t A256647 LinearRecurrence[{4, -6, 4, -1}, {0, 1, 28, 106}, 40] (* _Vincenzo Librandi_, Apr 08 2015 *)
%o A256647 (Magma) [n*(n+1)*(25*n-22)/6: n in [0..50]]; // _Vincenzo Librandi_, Apr 08 2015
%Y A256647 Partial sums of A255186.
%Y A256647 Cf. similar sequences listed in A237616.
%Y A256647 Cf. A000292, A256645.
%K A256647 nonn,easy
%O A256647 0,3
%A A256647 _Luciano Ancora_, Apr 07 2015