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 A382924 #10 Apr 10 2025 02:49:48
%S A382924 1,2,13,70,336,2076,11091,65210,365661,2159354,11713047,71427504,
%T A382924 392916687,2245186352,13527678851,73679458270,429472428457,
%U A382924 2553994191220,14264421153074,80483620074092,489077890675807,2768919905996888,15394229582049408,91794448088043258
%N A382924 Number of m-compositions of n with n zeros.
%C A382924 For some m > 0, an m-composition of n is a rectangular array of nonnegative integers with m rows, at least one nonzero entry in each column, and having the sum of all entries equal to n.
%F A382924 a(n) = [(x*t)^n] 1 + Sum_{m>0} -1 + 1/(1 + t^m - (t + x/(1 - x))^m).
%e A382924 a(2) = 13 counts:
%e A382924 [2] [0] [0] [1] [1] [1] [0] [0] [0] [1][1] [1][0] [0][0] [0][1]
%e A382924 [0] [2] [0] [1] [0] [0] [1] [1] [0] [0][0], [0][1], [1][1], [1][0].
%e A382924 [0], [0], [2], [0] [1] [0] [1] [0] [1]
%e A382924 [0], [0], [1], [0], [1], [1],
%o A382924 (PARI)
%o A382924 G_tx(max_row) = {my(row = max_row, N = row*2, m = List([concat([1],vector(row-1,i,0))]), x='x+O('x^N), h=1 + sum(m=1,N,-1+ 1/(1 + t^m - (t + x/(1-x))^m))); for(n=1,row, listput(m,Vecrev(polcoeff(h, n))[1..row])); matrix(row, row, i,j, m[i][j])}
%o A382924 A382924(max_n) ={my(A=G_tx(max_n)); vector(max_n,i,A[i,i])}
%o A382924 A382924(20)
%Y A382924 Cf. A038207, A101509, A181331, A261780, A323429, A382820, (main diagonal of A382923).
%K A382924 nonn
%O A382924 0,2
%A A382924 _John Tyler Rascoe_, Apr 09 2025