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 A074209 #22 Dec 06 2021 04:17:15
%S A074209 2,25,405,8418,216400,6668779,240361121,9936764996,463893277176,
%T A074209 24148657338925,1387253043076813,87185783860333910,
%U A074209 5951020164442347800,438417132703015536399,34673851743509883542625
%N A074209 a(n) = Sum_{i=n+1..2n} i^n.
%C A074209 A rapidly growing sequence. An even more rapidly growing sequence, the sum of next n terms of the form i^i, is given in A074309. Sum of first n terms of the form i^n is A031971. Sum of first n terms of the form i^i is A001923.
%H A074209 Seiichi Manyama, <a href="/A074209/b074209.txt">Table of n, a(n) for n = 1..351</a>
%F A074209 From _Wesley Ivan Hurt_, Jan 28 2021: (Start)
%F A074209 a(n) = Sum_{k=1..n} (n+k)^n.
%F A074209 a(n) = Zeta(-n,n+1) - Zeta(-n,2*n+1), where Zeta is the Hurwitz zeta function. (End)
%F A074209 a(n) ~ (2*n)^n / (1 - exp(-1/2)). - _Vaclav Kotesovec_, Dec 06 2021
%e A074209 a(2) = 25 = 3^2 + 4^2, a(3) = 405 = 4^3 + 5^3 + 6^3, a(4) = 8418 = 5^4 + 6^4 + 7^4 + 8^4, a(5) = 216400 = 6^4 + 7^5 + 8^5 + 9^5 + 10^5.
%t A074209 Table[Sum[i^n, {i, n+1, 2n}], {n, 20}]
%o A074209 (PARI) a(n) = sum(k=n+1, 2*n, k^n); \\ _Seiichi Manyama_, Dec 05 2021
%Y A074209 Cf. A001923, A031971, A074309.
%K A074209 nonn
%O A074209 1,1
%A A074209 _Zak Seidov_, Sep 22 2002
%E A074209 Name changed by _Wesley Ivan Hurt_, Jan 28 2021