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 A330151 #45 Mar 22 2024 17:48:33
%S A330151 0,16,272,1568,5664,15664,36400,74816,140352,245328,405328,639584,
%T A330151 971360,1428336,2042992,2852992,3901568,5237904,6917520,9002656,
%U A330151 11562656,14674352,18422448,22899904,28208320,34458320,41769936,50272992,60107488,71423984,84383984
%N A330151 Partial sums of 4th powers of the even numbers.
%H A330151 Colin Barker, <a href="/A330151/b330151.txt">Table of n, a(n) for n = 0..1000</a>
%H A330151 Abdelkarim Assoul, <a href="https://hal.archives-ouvertes.fr/hal-01924427">The sum of the natural numbers peers, odd of p-th degree</a>, hal-01924427, 2015.
%H A330151 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A330151 a(n) = Sum_{k=1..n} (2*k)^4 = (8/15)*n*(6*n^4 + 15*n^3 + 10*n^2 - 1).
%F A330151 a(n) = 16*A000538(n).
%F A330151 From _Colin Barker_, Dec 08 2019: (Start)
%F A330151 G.f.: 16*x*(1 + x)*(1 + 10*x + x^2) / (1 - x)^6.
%F A330151 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>5.
%F A330151 (End)
%F A330151 E.g.f.: (8/15)*exp(x)*x*(30 + 225*x + 250*x^2 + 75*x^3 + 6*x^4). - _Stefano Spezia_, Dec 08 2019
%F A330151 a(n+1) = 12*A002299(n) + A002492(n+1). - _Yasser Arath Chavez Reyes_, Mar 07 2024
%e A330151 a(4) = 0^4 + 2^4 + 4^4 + 6^4 + 8^4 = 5664.
%t A330151 a[n_] := (8/15)*n*(6*n^4 + 15*n^3 + 10*n^2 - 1); Array[a, 31, 0] (* _Amiram Eldar_, Dec 08 2019 *)
%o A330151 (PARI) a(n) = sum(i=0, n, 16*i^4); \\ _Jinyuan Wang_, Dec 07 2019
%o A330151 (PARI) concat(0, Vec(16*x*(1 + x)*(1 + 10*x + x^2) / (1 - x)^6 + O(x^30))) \\ _Colin Barker_, Dec 08 2019
%o A330151 (Python)
%o A330151 def A330151(n): return 8*n*(n**2*(n*(6*n + 15) + 10) - 1)//15 # _Chai Wah Wu_, Dec 07 2021
%Y A330151 Cf. A000538, A002309.
%Y A330151 Partial sums of A016744.
%K A330151 nonn,easy
%O A330151 0,2
%A A330151 _Assoul Abdelkarim_, Dec 03 2019
%E A330151 More terms from _Jinyuan Wang_, Dec 07 2019