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 A269951 #13 Feb 12 2025 09:27:08
%S A269951 1,0,1,0,2,1,0,5,5,1,0,16,23,9,1,0,65,116,65,14,1,0,326,669,470,145,
%T A269951 20,1,0,1957,4429,3634,1415,280,27,1,0,13700,33375,30681,14084,3535,
%U A269951 490,35,1,0,109601,283072,284066,147532,43939,7756,798,44,1
%N A269951 Triangle read by rows, T(n,k) = Sum_{j=0..n} (-1)^(n-j)*C(-j,-n)*S1(j,k), S1 the Stirling cycle numbers A132393, for n>=0 and 0<=k<=n.
%H A269951 Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/ExtensionsOfTheBinomial">Extensions of the binomial</a>
%e A269951 Triangle begins:
%e A269951 1;
%e A269951 0, 1;
%e A269951 0, 2, 1;
%e A269951 0, 5, 5, 1;
%e A269951 0, 16, 23, 9, 1;
%e A269951 0, 65, 116, 65, 14, 1;
%e A269951 0, 326, 669, 470, 145, 20, 1;
%p A269951 A269951 := (n,k) -> add((-1)^(n-j)*binomial(-j,-n)*abs(Stirling1(j,k)), j=0..n):
%p A269951 seq(seq(A269951(n,k), k=0..n), n=0..9);
%t A269951 Flatten[ Table[ Sum[(-1)^(n-j) Binomial[-j,-n] Abs[StirlingS1[j,k]], {j,0,n}], {n,0,9}, {k,0,n}]]
%Y A269951 A000522 (col. 1), A073596 (col. 2), A000096 (diag. n-1), A241765 (diag. n-2).
%Y A269951 A001339 (row sums), A137597 (unsigned matrix inverse).
%Y A269951 Cf. A132393, A269952.
%K A269951 nonn,tabl
%O A269951 0,5
%A A269951 _Peter Luschny_, Apr 10 2016