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 A134399 #16 May 03 2024 08:27:40
%S A134399 1,1,1,1,2,2,1,3,6,3,1,4,12,12,4,1,5,20,30,20,5,1,6,30,60,60,30,6,1,7,
%T A134399 42,105,140,105,42,7,1,8,56,168,280,280,168,56,8,1,9,72,252,504,630,
%U A134399 504,252,72,9
%N A134399 Matrix product of Binomial triangle A007318 and triangle with (1, 1, 2, 3, 4, 5, ...) in the main diagonal and the rest zeros.
%C A134399 Row sums = A005183: (1, 2, 5, 13, 33, 81, 193, ...).
%F A134399 T(n,0) = 1; T(n,k) = k*binomial(n,k) for 1 <= k <= n. [corrected by _Paolo Xausa_, May 03 2024]
%e A134399 First few rows of the triangle:
%e A134399 1;
%e A134399 1, 1;
%e A134399 1, 2, 2;
%e A134399 1, 3, 6, 3;
%e A134399 1, 4, 12, 12, 4;
%e A134399 1, 5, 20, 30, 20, 5;
%e A134399 1, 6, 30, 60, 60, 30, 6;
%e A134399 1, 7, 42, 105, 140, 105, 42, 7;
%e A134399 ...
%t A134399 Table[Max[k, 1]*Binomial[n, k], {n, 0, 10}, {k, 0, n}] (* _Paolo Xausa_, May 03 2024 *)
%Y A134399 Cf. A005183, A007318.
%K A134399 nonn,tabl
%O A134399 0,5
%A A134399 _Gary W. Adamson_, Oct 23 2007
%E A134399 Corrected and edited by _Olivier Gérard_, Aug 01 2013