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 A254463 #26 Sep 16 2024 16:54:13
%S A254463 56,126,378,1386,5778,26226,126378,636426,3314178,17714466,96660378,
%T A254463 536249466,3015243378,17141522706,98333399178,568324150506,
%U A254463 3305074833378,19319850386946,113420243462778,668241096915546,3948892688324178,23393955029043186,138880128205091178
%N A254463 a(n) = 15*2^n + 6*4^n + 10*3^n + 3*5^n + 6^n + 21.
%C A254463 This is the sequence of sixth terms of "third partial sums of m-th powers".
%H A254463 Colin Barker, <a href="/A254463/b254463.txt">Table of n, a(n) for n = 0..1000</a>
%H A254463 Luciano Ancora, <a href="https://oeis.org/A254364/a254364.pdf">Demonstration of formulas</a>, page 2.
%H A254463 Luciano Ancora, <a href="/A254364/a254364_1.pdf">Recurrence relations for partial sums of m-th powers</a>.
%H A254463 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (21,-175,735,-1624,1764,-720).
%F A254463 From _Colin Barker_, Jan 31 2015: (Start)
%F A254463 G.f.: -2*(12276*x^5 - 20578*x^4 + 12831*x^3 - 3766*x^2 + 525*x - 28)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)).
%F A254463 a(n) = 21*a(n-1) - 175*a(n-2) + 735*a(n-3) - 1624*a(n-4) + 1764*a(n-5) - 720*a(n-6). (End)
%F A254463 E.g.f.: exp(x)*(exp(5*x) + 3*exp(4*x) + 6*exp(3*x) + 10*exp(2*x) + 15*exp(x) + 21). - _Elmo R. Oliveira_, Sep 16 2024
%t A254463 Table[15 2^n + 6 4^n + 10 3^n + 3 5^n + 6^n + 21, {n, 0, 25}] (* _Michael De Vlieger_, Jan 31 2015 *)
%o A254463 (PARI) vector(30, n, n--; 15*2^n + 6*4^n + 10*3^n + 3*5^n + 6^n + 21) \\ _Colin Barker_, Jan 31 2015
%Y A254463 Cf. A062709, A254362, A254363, A254364, A254464.
%K A254463 nonn,easy
%O A254463 0,1
%A A254463 _Luciano Ancora_, Jan 31 2015