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 A174712 #26 Jul 25 2024 14:01:31
%S A174712 1,0,1,0,0,2,0,0,0,3,0,0,0,0,5,0,0,0,0,0,7,0,0,0,0,0,0,11,0,0,0,0,0,0,
%T A174712 0,15,0,0,0,0,0,0,0,0,22,0,0,0,0,0,0,0,0,0,30,0,0,0,0,0,0,0,0,0,0,42,
%U A174712 0,0,0,0,0,0,0,0,0,0,0,56,0,0,0,0,0,0,0,0,0,0,0,0,77
%N A174712 Triangle T(n,k) read by rows in which the right border is A000041, else zero, n >= 0.
%C A174712 Eigensequence of the triangle = A058694: (1, 1, 2, 6, 30, 210,...), i.e., given A058694 preceded by a "1", triangle A174712 * the latter variant = the same sequence but shifted left.
%H A174712 Paolo Xausa, <a href="/A174712/b174712.txt">Table of n, a(n) for n = 0..11475</a> (rows 0..150 of the triangle, flattened).
%e A174712 Triangle begins:
%e A174712 1;
%e A174712 0, 1;
%e A174712 0, 0, 2;
%e A174712 0, 0, 0, 3;
%e A174712 0, 0, 0, 0, 5;
%e A174712 0, 0, 0, 0, 0, 7;
%e A174712 0, 0, 0, 0, 0, 0, 11;
%e A174712 0, 0, 0, 0, 0, 0, 0, 15;
%e A174712 0, 0, 0, 0, 0, 0, 0, 0, 22;
%e A174712 0, 0, 0, 0, 0, 0, 0, 0, 0, 30;
%e A174712 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 42;
%e A174712 ...
%t A174712 Array[PadLeft[{PartitionsP[#-1]}, #] &, 15] (* _Paolo Xausa_, Feb 21 2024 *)
%Y A174712 Cf. A000041, A058694, A174713, A174714, A174715.
%K A174712 nonn,tabl
%O A174712 0,6
%A A174712 _Gary W. Adamson_, Mar 27 2010
%E A174712 Definition clarified by _Omar E. Pol_, Feb 21 2024