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 A254031 #29 Jan 24 2022 16:47:36
%S A254031 15,35,105,371,1449,6035,26265,117971,542409,2538515,12044025,
%T A254031 57756371,279305769,1359736595,6654800985,32708239571,161307227529,
%U A254031 797687136275,3953299529145,19626731023571,97576919443689,485664640673555
%N A254031 a(n) = 1*5^n + 2*4^n + 3*3^n + 4*2^n + 5*1^n.
%C A254031 This is the sequence of fifth terms of "second partial sums of m-th powers".
%H A254031 Colin Barker, <a href="/A254031/b254031.txt">Table of n, a(n) for n = 0..1000</a>
%H A254031 Luciano Ancora, <a href="/A254031/a254031_1.pdf">Demonstration of formulas</a>
%H A254031 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (15,-85,225,-274,120).
%F A254031 G.f.: -(1044*x^4 - 1604*x^3 + 855*x^2 - 190*x + 15) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)). - _Colin Barker_, Jan 26 2015
%F A254031 From _Peter Bala_, Jan 31 2016: (Start)
%F A254031 a(n) = (x + 1)*( Bernoulli(n + 1, x + 1) - Bernoulli(n + 1, 1) )/(n + 1) - ( Bernoulli(n + 2, x + 1) - Bernoulli(n + 2, 1) )/(n + 2) at x = 5.
%F A254031 a(n) = (1/4!)*Sum_{k = 0..n} (-1)^(k+n)*(k + 6)!*Stirling2(n,k)/
%F A254031 ((k + 1)*(k + 2)). (End)
%p A254031 seq(add(i*(6 - i)^n, i = 1..5), n = 0..20); # _Peter Bala_, Jan 31 2017
%t A254031 Table[2^(n + 2) + 2^(2 n + 1) + 3^(n + 1) + 5^n + 5, {n, 0, 25}] (* _Bruno Berselli_, Jan 27 2015 *)
%t A254031 LinearRecurrence[{15,-85,225,-274,120},{15,35,105,371,1449},30] (* _Harvey P. Dale_, Jan 24 2022 *)
%o A254031 (PARI) Vec(-(1044*x^4-1604*x^3+855*x^2-190*x+15)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)) + O(x^100)) \\ _Colin Barker_, Jan 26 2015
%Y A254031 Cf. A052548, A254028, A254030, A254144, A254145, A254146.
%K A254031 nonn,easy
%O A254031 0,1
%A A254031 _Luciano Ancora_, Jan 26 2015