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 A265021 #30 Sep 08 2022 08:46:14
%S A265021 0,32,1056,8832,41600,141600,390432,928256,1976832,3866400,7066400,
%T A265021 12220032,20182656,32064032,49274400,73574400,107128832,152564256,
%U A265021 213030432,292265600,394665600,525356832,690273056,896236032,1151040000,1463540000,1843744032
%N A265021 Sum of fifth powers of the first n even numbers.
%H A265021 G. C. Greubel, <a href="/A265021/b265021.txt">Table of n, a(n) for n = 0..1000</a>
%H A265021 Assoul Abdelkarim, <a href="/A265021/a265021.pdf">The sums of powers of integers natural even, odd</a>, RMSS-D-15-00105.
%H A265021 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A265021 a(n) = 32 * Sum_{i=0..n} i^5 = (8/3)*n^2*(n+1)^2*(2*n^2+2*n-1).
%F A265021 a(n) = 32 * A000539(n).
%F A265021 G.f.: 32*x*(1 + 26*x + 66*x^2 + 26*x^3 + x^4)/(1-x)^7. - _Vincenzo Librandi_, Dec 01 2015
%F A265021 a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7). - _Vincenzo Librandi_, Dec 01 2015
%e A265021 a(4) = 2^5 + 4^5 + 6^5 + 8^5 = 41600.
%t A265021 Accumulate[Range[0, 60, 2]^5] (* _Michael De Vlieger_, Nov 30 2015 *)
%t A265021 CoefficientList[Series[32 x (1 + 26 x + 66 x^2 + 26 x^3 + x^4)/(1 - x)^7, {x, 0, 33}], x] (* _Vincenzo Librandi_, Dec 01 2015 *)
%o A265021 (Magma) [(8/3)*n^2*(n+1)^2*(2*n^2+2*n-1): n in [0..30]]; // _Vincenzo Librandi_, Dec 01 2015
%o A265021 (PARI) vector(100, n, n--; (8/3)*n^2*(n+1)^2*(2*n^2+2*n-1)) \\ _Altug Alkan_, Dec 01 2015
%Y A265021 Cf. A000539, A002594 (the same for odd numbers).
%K A265021 nonn
%O A265021 0,2
%A A265021 _Assoul Abdelkarim_, Nov 30 2015