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 A382820 #7 Apr 06 2025 08:45:09
%S A382820 1,11,163,3019,67251,1753877,52468711,1772042699,66708748963,
%T A382820 2770212058261,125812351808551,6203908746628501,330108021642012407,
%U A382820 18853083403505443593,1150352428059538611663,74685045367715777653195,5140745255774277374241411,373950591013899715795929605
%N A382820 Number of columns in all n-compositions of n.
%C A382820 A k-composition of n is a rectangular array of nonnegative integers with k rows, at least one nonzero entry in each column, and having the sum of all entries equal to n.
%F A382820 a(n) = [x^n] -((1 - x)^n - 1)*(1 - x)^n/(((1 - x)^n - 1) + (1 - x)^n)^2
%o A382820 (PARI)
%o A382820 A382818_Column(k,N) = {my(x='x+O('x^N)); Vec(-(((1 - x)^k - 1)*(1 - x)^k)/( ((1 - x)^k - 1) + (1 - x)^k)^2)}
%o A382820 A382820(n)= {A382818_Column(n,n+1)[n]}
%Y A382820 C.f. A001792, A145839, A181289, A181290, (main diagonal of A382818).
%K A382820 nonn,easy
%O A382820 1,2
%A A382820 _John Tyler Rascoe_, Apr 05 2025