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 A189122 #18 Sep 08 2022 08:45:56
%S A189122 1,5,45,526,7585,130371,2602285,59142588,1507308129,42563286145,
%T A189122 1318792866941,44477806954890,1621859437812289,63576780042697663,
%U A189122 2665971232476845805,119073945060707737336,5643402849491554535745
%N A189122 a(n) = Sum_{i=0..n} (i+1)^2*n^i.
%D A189122 "Supplemento al Periodico di Matematica", Raffaello Giusti Editore (Livorno), Apr/May 1913 p. 99 (Problem 1277, case x=n).
%H A189122 Bruno Berselli, <a href="/A189122/b189122.txt">Table of n, a(n) for n = 0..300</a>
%F A189122 a(n) = (n+1)*(4*n^(n+1)-3*n^(n+2)-n^(n+3)+n^(n+4)-1)/(n-1)^3 for n>1; a(0)=1, a(1)=5.
%e A189122 a(4) = 7585 because 7585 = 1+2^2*4+3^2*4^2+4^2*4^3+5^2*4^4.
%t A189122 Join[{1, 5}, Table[(n + 1) (4 n^(n + 1) - 3 n^(n + 2) - n^(n + 3) + n^(n + 4) -1) / (n - 1)^3, {n, 2, 20}]] (* _Vincenzo Librandi_, Aug 19 2013 *)
%o A189122 (Magma) [&+[(k+1)^2*n^k: k in [0..n]]: n in [0..17]];
%Y A189122 Cf. A062806, A189001.
%K A189122 nonn,easy
%O A189122 0,2
%A A189122 _Bruno Berselli_, Apr 19 2011