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 A254364 #29 Sep 16 2024 16:54:03
%S A254364 35,70,182,574,2054,7990,32942,141694,629174,2862790,13275902,
%T A254364 62494414,297701894,1431677590,6937683662,33825224734,165731728214,
%U A254364 815255212390,4023182840222,19905098860654,98686897716134,490094080827190,2437150677449582,12132600130570174,60450764450513654
%N A254364 a(n) = 3*4^n + 10*2^n + 6*3^n + 5^n + 15.
%C A254364 This is the sequence of fifth terms of "third partial sums of m-th powers".
%H A254364 Colin Barker, <a href="/A254364/b254364.txt">Table of n, a(n) for n = 0..1000</a>
%H A254364 Luciano Ancora, <a href="https://oeis.org/A254364/a254364.pdf">Demonstration of formulas</a>, page 2.
%H A254364 Luciano Ancora, <a href="/A254364/a254364_1.pdf">Recurrence relations for partial sums of m-th powers</a>.
%H A254364 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (15,-85,225,-274,120).
%F A254364 From _Colin Barker_, Jan 30 2015: (Start)
%F A254364 G.f.: -(2754*x^4 - 4081*x^3 + 2107*x^2 - 455*x + 35)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)).
%F A254364 a(n) = 15*a(n-1) - 85*a(n-2) + 225*a(n-3) - 274*a(n-4) + 120*a(n-5). (End)
%F A254364 E.g.f.: exp(x)*(exp(4*x) + 3*exp(3*x) + 6*exp(2*x) + 10*exp(x) + 15). - _Elmo R. Oliveira_, Sep 16 2024
%t A254364 Table[3 4^n + 10 2^n + 6 3^n + 5^n + 15, {n, 0, 30}] (* _Bruno Berselli_, Jan 30 2015 *)
%t A254364 LinearRecurrence[{15,-85,225,-274,120},{35,70,182,574,2054},30] (* _Harvey P. Dale_, Aug 11 2016 *)
%o A254364 (PARI) vector(30, n, n--; 3*4^n + 10*2^n + 6*3^n + 5^n + 15) \\ _Colin Barker_, Jan 30 2015
%Y A254364 Cf. A062709, A254362, A254363.
%K A254364 nonn,easy
%O A254364 0,1
%A A254364 _Luciano Ancora_, Jan 29 2015