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 A037205 #57 Dec 16 2022 09:02:40
%S A037205 0,1,8,63,624,7775,117648,2097151,43046720,999999999,25937424600,
%T A037205 743008370687,23298085122480,793714773254143,29192926025390624,
%U A037205 1152921504606846975,48661191875666868480,2185911559738696531967,104127350297911241532840,5242879999999999999999999,278218429446951548637196400,15519448971100888972574851071
%N A037205 a(n) = (n+1)^n - 1.
%C A037205 For n >= 1, a(n) = order of Fibonacci group F(n+1,n).
%C A037205 The terms, written in base n+1, are n digits of value n. For example, a(4) = 624 = 4444 in base 5. - _Marc Morgenegg_, Nov 30 2016
%C A037205 For n >= 1, in a square grid of side n, this is the number of ways to populate the grid with 1 X 1 blocks (with at least one block) so that no block falls under the effect of gravity. - _Paolo Xausa_, Apr 12 2021
%C A037205 For n > 1, (n-1)^2 | a(n). - _David A. Corneth_, Dec 15 2022
%D A037205 D. L. Johnson, Presentation of Groups, Cambridge, 1976, p. 182.
%D A037205 Richard M. Thomas, The Fibonacci groups revisited, in Groups - St. Andrews 1989, Vol. 2, 445-454, London Math. Soc. Lecture Note Ser., 160, Cambridge Univ. Press, Cambridge, 1991.
%H A037205 G. C. Greubel, <a href="/A037205/b037205.txt">Table of n, a(n) for n = 0..385</a>
%H A037205 Michael Penn, <a href="https://www.youtube.com/watch?v=cW5o4Z2nPzo">A divisibility problem.</a>, YouTube video, 2021.
%F A037205 a(n) = A000169(n+1) - 1 = A060072(n+1)*(n-1) = A060073(n+1)*(n-1)^2.
%F A037205 E.g.f.: 1/(exp(LambertW(-x)) - x) - exp(x). - _Ilya Gutkovskiy_, Nov 30 2016
%F A037205 E.g.f.: -exp(x) - 1/(x + x/LambertW(-x)). - _Vaclav Kotesovec_, Dec 05 2016
%F A037205 a(n) = Sum_{k=1..n} binomial(n,k)*n^k [from _Paolo Xausa_'s comment]. - _Joerg Arndt_, Apr 12 2021
%t A037205 Table[(n + 1)^n - 1, {n, 0, 21}] (* or *)
%t A037205 Table[If[n < 1, Length@ #, FromDigits[#, n + 1]] &@ ConstantArray[n, n], {n, 0, 21}] (* _Michael De Vlieger_, Nov 30 2016 *)
%o A037205 (PARI) for(n=0,25, print1((n + 1)^n - 1, ", ")) \\ _G. C. Greubel_, Nov 10 2017
%o A037205 (Magma) [(n + 1)^n - 1: n in [0..25]]; // _G. C. Greubel_, Nov 10 2017
%Y A037205 A diagonal of A202624.
%K A037205 nonn,easy
%O A037205 0,3
%A A037205 _N. J. A. Sloane_
%E A037205 Revised by _N. J. A. Sloane_, Dec 30 2011