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 A276719 #28 Dec 27 2018 16:30:04
%S A276719 1,1,0,1,1,0,1,1,1,0,1,1,2,1,0,1,1,2,3,1,0,1,1,2,5,5,1,0,1,1,2,5,10,8,
%T A276719 1,0,1,1,2,5,15,20,13,1,0,1,1,2,5,15,37,42,21,1,0,1,1,2,5,15,52,87,87,
%U A276719 34,1,0,1,1,2,5,15,52,151,208,179,55,1,0,1,1,2,5,15,52,203,409,515,370,89,1,0
%N A276719 Number A(n,k) of set partitions of [n] such that for each block b the smallest integer interval containing b has at most k elements; square array A(n,k), n>=0, k>=0, read by antidiagonals.
%C A276719 The sequence of column k satisfies a linear recurrence with constant coefficients of order 2^(k-1) for k>0.
%H A276719 Alois P. Heinz, <a href="/A276719/b276719.txt">Antidiagonals n = 0..40, flattened</a>
%H A276719 Pierpaolo Natalini, Paolo Emilio Ricci, <a href="https://doi.org/10.3390/axioms7040071">New Bell-Sheffer Polynomial Sets</a>, Axioms 2018, 7(4), 71.
%H A276719 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A276719 A(n,k) = Sum_{i=0..k} A276727(n,i).
%e A276719 A(3,2) = 3: 12|3, 1|23, 1|2|3.
%e A276719 A(4,3) = 10: 123|4, 12|34, 12|3|4, 13|24, 13|2|4, 1|234, 1|23|4, 1|24|3, 1|2|34, 1|2|3|4.
%e A276719 A(5,4) = 37: 1234|5, 123|45, 123|4|5, 124|35, 124|3|5, 12|345, 12|34|5, 12|35|4, 12|3|45, 12|3|4|5, 134|25, 134|2|5, 13|245, 13|24|5, 13|25|4, 13|2|45, 13|2|4|5, 14|235, 14|23|5, 1|2345, 1|234|5, 1|235|4, 1|23|45, 1|23|4|5, 14|25|3, 14|2|35, 14|2|3|5, 1|245|3, 1|24|35, 1|24|3|5, 1|25|34, 1|2|345, 1|2|34|5, 1|25|3|4, 1|2|35|4, 1|2|3|45, 1|2|3|4|5.
%e A276719 Square array A(n,k) begins:
%e A276719 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A276719 0, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A276719 0, 1, 2, 2, 2, 2, 2, 2, 2, ...
%e A276719 0, 1, 3, 5, 5, 5, 5, 5, 5, ...
%e A276719 0, 1, 5, 10, 15, 15, 15, 15, 15, ...
%e A276719 0, 1, 8, 20, 37, 52, 52, 52, 52, ...
%e A276719 0, 1, 13, 42, 87, 151, 203, 203, 203, ...
%e A276719 0, 1, 21, 87, 208, 409, 674, 877, 877, ...
%e A276719 0, 1, 34, 179, 515, 1100, 2066, 3263, 4140, ...
%p A276719 b:= proc(n, m, l) option remember; `if`(n=0, 1,
%p A276719 add(b(n-1, max(m, j), [subsop(1=NULL, l)[],
%p A276719 `if`(j<=m, 0, j)]), j={l[], m+1} minus {0}))
%p A276719 end:
%p A276719 A:= (n, k)-> `if`(n=0, 1, `if`(k<2, k, b(n, 0, [0$(k-1)]))):
%p A276719 seq(seq(A(n, d-n), n=0..d), d=0..14);
%t A276719 b[n_, m_, l_List] := b[n, m, l] = If[n == 0, 1, Sum[b[n - 1, Max[m, j], Append[ReplacePart[l, 1 -> Nothing], If[j <= m, 0, j]]], {j, Append[l, m + 1] ~Complement~ {0}}]]; A[n_, k_] := If[n == 0, 1, If[k < 2, k, b[n, 0, Array[0&, k-1]]]]; Table[A[n, d-n], {d, 0, 14}, {n, 0, d}] // Flatten (* _Jean-François Alcover_, Jan 06 2017, after _Alois P. Heinz_ *)
%Y A276719 Columns k=0..10 give: A000007, A000012, A000045(n+1), A129847, A276720, A276721, A276722, A276723, A276724, A276725, A276726.
%Y A276719 Main diagonal gives A000110.
%Y A276719 A(n+1,n) gives A005493(n-1) for n>0.
%Y A276719 Cf. A276727, A276837.
%K A276719 nonn,tabl
%O A276719 0,13
%A A276719 _Alois P. Heinz_, Sep 16 2016