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 A155742 #10 Sep 08 2022 08:45:41
%S A155742 1,0,0,0,1,0,0,6,6,0,0,36,121,36,0,0,240,1750,1750,240,0,0,1800,23290,
%T A155742 50625,23290,1800,0,0,15120,308700,1193640,1193640,308700,15120,0,0,
%U A155742 141120,4207896,25738720,45819361,25738720,4207896,141120,0,0,1451520,59832864,535810464,1510458516,1510458516,535810464,59832864,1451520,0
%N A155742 Triangle T(n, k) = (-1)^n*StirlingS1(n, k)*StirlingS1(n, n-k), read by rows.
%H A155742 G. C. Greubel, <a href="/A155742/b155742.txt">Rows n = 0..50 of the triangle flattened</a>
%F A155742 T(n, k) = (-1)^n*StirlingS1(n, k)*StirlingS1(n, n-k).
%F A155742 Sum_{k=0..n} T(n, k) = A342111(n). - _G. C. Greubel_, Jun 05 2021
%e A155742 Triangle begins as:
%e A155742 1;
%e A155742 0, 0;
%e A155742 0, 1, 0;
%e A155742 0, 6, 6, 0;
%e A155742 0, 36, 121, 36, 0;
%e A155742 0, 240, 1750, 1750, 240, 0;
%e A155742 0, 1800, 23290, 50625, 23290, 1800, 0;
%e A155742 0, 15120, 308700, 1193640, 1193640, 308700, 15120, 0;
%e A155742 0, 141120, 4207896, 25738720, 45819361, 25738720, 4207896, 141120, 0;
%t A155742 T[n_, k_]:= (-1)^n*StirlingS1[n, k]*StirlingS1[n, n-k];
%t A155742 Table[T[n, k], {n,0,12}, {k,0,n}]//Flatten (* modified by _G. C. Greubel_, Jun 05 2021 *)
%o A155742 (Magma)
%o A155742 A155742:= func< n,k | (-1)^n*StirlingFirst(n, k)*StirlingFirst(n, n-k) >;
%o A155742 [A155742(n,k): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Jun 05 2021
%o A155742 (Sage)
%o A155742 def A155742(n,k): return stirling_number1(n,k)*stirling_number1(n, n-k)
%o A155742 flatten([[A155742(n,k) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Jun 05 2021
%Y A155742 Cf. A048994, A342111 (row sums).
%K A155742 nonn,tabl
%O A155742 0,8
%A A155742 _Roger L. Bagula_, Jan 26 2009
%E A155742 Edited by _G. C. Greubel_, Jun 05 2021