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 A367198 #19 Nov 10 2023 18:01:55
%S A367198 1,1,2,4,6,3,15,30,18,4,76,165,125,40,5,455,1075,930,380,75,6,3186,
%T A367198 8015,7679,3675,945,126,7,25487,67536,70042,37688,11550,2044,196,8,
%U A367198 229384,634935,702372,414078,144417,30870,3990,288,9,2293839,6591943,7696245,4886390,1885065,463092,73080,7200,405,10
%N A367198 T(n, k) = Sum_{m = 0..n-1} Stirling1(m+1, k)*binomial(n, m)*(-1)^(n + k), where "Stirling1" are the signed Stirling numbers of the first kind.
%C A367198 To use the unsigned Stirling numbers rewrite the formula as: T(n, k) = Sum_{m = 0..n-1} abs(Stirling1(m+1, k))*binomial(n, m)*(-1)^(1+m+n). Replacing in this formula Stirling1 (A008275) by Stirling2 (A048993) one obtains a shifted version of A321331.
%F A367198 T(n+1, n) = n^2*(n+1)/2 = A002411(n).
%F A367198 T(n, n-2) = 6*T(n-1, n-3) - 15*T(n-2, n-4) + 20*T(n-3, n-5) - 15*T(n-4, n-6) + 6*T(n-5, n-7) - T(n-6, n-8), for n > 8.
%F A367198 T(n, n-k) = (-1)^k*Sum_{m=0..n-1} Stirling1(m+1, n-k)*binomial(n, m).
%e A367198 Triangle begins:
%e A367198 1;
%e A367198 1, 2;
%e A367198 4, 6, 3;
%e A367198 15, 30, 18, 4;
%e A367198 76, 165, 125, 40, 5;
%e A367198 455, 1075, 930, 380, 75, 6;
%p A367198 T := (n, k) -> local m; add(Stirling1(m+1, k)*binomial(n, m)*(-1)^(n + k), m = 0..n-1): seq(seq(T(n, k), k = 1..n), n = 1..9); # _Peter Luschny_, Nov 10 2023
%o A367198 (PARI) T(n,k) = sum(m=0, n-1, stirling(m+1, k)*binomial(n, m)*(-1)^(n+k))
%Y A367198 Cf. A002411, A002467 (first column), A000027 (main diagonal), A008275.
%Y A367198 Cf. A180191(n+1) (row sums), A321331 (variant with Stirling2).
%K A367198 nonn,tabl
%O A367198 1,3
%A A367198 _Thomas Scheuerle_, Nov 10 2023