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 A359759 #13 Jan 28 2023 12:17:09
%S A359759 1,0,1,0,-3,1,0,13,-9,1,0,-103,79,-18,1,0,1241,-905,265,-30,1,0,
%T A359759 -19691,13771,-4290,665,-45,1,0,384805,-262885,82621,-14630,1400,-63,
%U A359759 1,0,-8918351,6007247,-1888362,353381,-40390,2618,-84,1
%N A359759 Table read by rows. T(n, k) = (-1)^(n - k) * Sum_{j=k..n} binomial(n, j) * A354794(j, k) * j^(n - j).
%C A359759 Inspired by a formula of _Mélika Tebni_ in A048993.
%F A359759 E.g.f. of column k: (exp(LambertW(x*exp(-x))) - 1)^k / k!. (Note that (exp(-LambertW(-x*exp(-x))) - 1)^k / k! is the e.g.f. of column k of Stirling2.) - _Mélika Tebni_, Jan 27 2023
%e A359759 Triangle T(n, k) starts:
%e A359759 [0] 1;
%e A359759 [1] 0, 1;
%e A359759 [2] 0, -3, 1;
%e A359759 [3] 0, 13, -9, 1;
%e A359759 [4] 0, -103, 79, -18, 1;
%e A359759 [5] 0, 1241, -905, 265, -30, 1;
%e A359759 [6] 0, -19691, 13771, -4290, 665, -45, 1;
%e A359759 [7] 0, 384805, -262885, 82621, -14630, 1400, -63, 1;
%e A359759 [8] 0, -8918351, 6007247, -1888362, 353381, -40390, 2618, -84, 1;
%e A359759 [9] 0, 238966705, -159432369, 50110705, -9627702, 1206471, -96138, 4494, -108, 1;
%p A359759 T := (n, k) -> (-1)^(n - k)*add(binomial(n, j) * A354794(j, k) * j^(n - j), j = k..n): for n from 0 to 9 do seq(T(n, k), k = 0..n) od;
%Y A359759 Cf. A059297, A354794, A357247, A048993.
%K A359759 sign,tabl
%O A359759 0,5
%A A359759 _Peter Luschny_, Jan 27 2023