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 A238341 #26 Jan 19 2015 03:43:18
%S A238341 1,0,1,0,1,1,0,3,0,1,0,6,1,0,1,0,12,3,0,0,1,0,23,7,1,0,0,1,0,46,13,4,
%T A238341 0,0,0,1,0,91,25,10,1,0,0,0,1,0,183,46,21,5,0,0,0,0,1,0,367,89,39,15,
%U A238341 1,0,0,0,0,1,0,737,175,70,35,6,0,0,0,0,0,1,0,1478,351,125,71,21,1,0,0,0,0,0,1
%N A238341 Triangle T(n,k) read by rows: T(n,k) is the number of compositions of n with exactly k occurrences of the largest part, n>=0, 0<=k<=n.
%C A238341 Columns k=0-10 give: A000007, A097979(n-1) for n>0, A243737, A243738, A243739, A243740, A243741, A243742, A243743, A243744, A243745.
%C A238341 T(n^2,n) gives A243746(n).
%C A238341 Row sums are A011782.
%H A238341 Joerg Arndt and Alois P. Heinz, <a href="/A238341/b238341.txt">Rows n = 0..140, flattened</a>
%e A238341 Triangle starts:
%e A238341 00: 1;
%e A238341 01: 0, 1;
%e A238341 02: 0, 1, 1;
%e A238341 03: 0, 3, 0, 1;
%e A238341 04: 0, 6, 1, 0, 1;
%e A238341 05: 0, 12, 3, 0, 0, 1;
%e A238341 06: 0, 23, 7, 1, 0, 0, 1;
%e A238341 07: 0, 46, 13, 4, 0, 0, 0, 1;
%e A238341 08: 0, 91, 25, 10, 1, 0, 0, 0, 1;
%e A238341 09: 0, 183, 46, 21, 5, 0, 0, 0, 0, 1;
%e A238341 10: 0, 367, 89, 39, 15, 1, 0, 0, 0, 0, 1;
%e A238341 11: 0, 737, 175, 70, 35, 6, 0, 0, 0, 0, 0, 1;
%e A238341 12: 0, 1478, 351, 125, 71, 21, 1, 0, 0, 0, 0, 0, 1;
%e A238341 13: 0, 2962, 710, 229, 131, 56, 7, 0, 0, 0, 0, 0, 0, 1;
%e A238341 14: 0, 5928, 1443, 435, 230, 126, 28, 1, 0, 0, 0, 0, 0, 0, 1,
%e A238341 15: 0, 11858, 2926, 859, 395, 253, 84, 8, 0, 0, 0, 0, 0, 0, 0, 1;
%e A238341 ...
%t A238341 b[n_, p_, i_] := b[n, p, i] = If[n == 0, p!, If[i<1, 0, Sum[b[n-i*j, p+j, i-1]/j!, {j, 0, n/i}]]]; a[n_, k_] := Sum[b[n-i*k, k, i-1]/k!, {i, 1, n/k}]; a[0, 0] = 1; a[_, 0] = 0; Table[a[n, k], {n, 0, 15}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Jan 19 2015, after Maple code in A243737 *)
%Y A238341 Cf. A026794 (the same for partitions), A238342 (the same for smallest part).
%K A238341 nonn,tabl
%O A238341 0,8
%A A238341 _Joerg Arndt_ and _Alois P. Heinz_, Feb 25 2014