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 A123081 #21 Sep 08 2022 08:45:28
%S A123081 1,1,1,2,2,2,5,5,5,5,15,15,15,15,15,52,52,52,52,52,52,203,203,203,203,
%T A123081 203,203,203,877,877,877,877,877,877,877,877,4140,4140,4140,4140,4140,
%U A123081 4140,4140,4140,4140,21147,21147,21147,21147,21147,21147,21147,21147,21147,21147,115975,115975,115975,115975
%N A123081 Infinite square array read by antidiagonals: T(n,k) = Bell(n+k) = A000110(n+k).
%C A123081 Alternatively, triangle read by rows in which row n (n >= 0) contains A000110(n) repeated n+1 times.
%C A123081 Row sums = A052887: 1, 2, 6, 20, 75, 312, ... A127568 = Q * M n-th row is composed of n+1 terms of A000110(n).
%H A123081 G. C. Greubel, <a href="/A123081/b123081.txt">Antidiagonal rows n = 0..50, flattened</a>
%H A123081 W. F. Lunnon et al., <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa35/aa3511.pdf">Arithmetic properties of Bell numbers to a composite modulus I</a>, Acta Arith., 35 (1979), 1-16. [From _N. J. A. Sloane_, Feb 07 2009]
%F A123081 M * Q, as infinite lower triangular matrices; M = the Bell sequence, A000110 in the main diagonal and the rest zeros. Q = (1; 1, 1; 1, 1, 1; ...)
%e A123081 Square array begins:
%e A123081 1, 1, 2, 5, 15, 52, 203, 877, ...;
%e A123081 1, 2, 5, 15, 52, 203, 877, 4140, ...;
%e A123081 2, 5, 15, 52, 203, 877, 4140, 21147, ...;
%e A123081 5, 15, 52, 203, 877, 4140, 21147, 115975, ...;
%e A123081 15, 52, 203, 877, 4140, 21147, 115975, 678570, ...;
%e A123081 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, ...;
%e A123081 203, 877, 4140, 21147, 115975, 678570, 4213597, 27644437, ...;
%e A123081 877, 4140, 21147, 115975, 678570, 4213597, 27644437, 190899322, ...;
%e A123081 First few rows of the triangle:
%e A123081 1;
%e A123081 1, 1;
%e A123081 2, 2, 2;
%e A123081 5, 5, 5, 5;
%e A123081 15, 15, 15, 15, 15;
%e A123081 52, 52, 52, 52, 52, 52;
%e A123081 203, 203, 203, 203, 203, 203, 203;
%t A123081 Table[BellB[n], {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, Jul 21 2021 *)
%o A123081 (PARI) B(n)=sum(k=0,n,stirling(n,k,2));
%o A123081 for(n=0,20,for(k=0,n,print1(B(n),", "))); \\ _Joerg Arndt_, Apr 21 2014
%o A123081 (Magma) [Bell(n): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Jul 21 2021
%o A123081 (Sage) flatten([[bell_number(n) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Jul 21 2021
%Y A123081 Cf. A000110, A052887, A127568.
%K A123081 nonn,easy,tabl
%O A123081 0,4
%A A123081 _Gary W. Adamson_, Jan 19 2007
%E A123081 Edited by _N. J. A. Sloane_, Feb 07 2009
%E A123081 Added more terms, _Joerg Arndt_, Apr 21 2014