%I #20 Jan 10 2024 04:57:28
%S 1,1,1,1,2,1,1,5,4,1,1,13,17,7,1,1,39,75,45,11,1,1,151,364,290,100,16,
%T 1,1,783,2065,1974,875,196,22,1,1,5167,14034,14833,7819,2226,350,29,1,
%U 1,40575,112609,125894,74235,25095,4998,582,37,1,1,363391,1035906,1206805
%N Triangle read by rows: T(n,k) = Stirling2(n, k+1) + abs(Stirling1(n,k)), 0 <= k <= n.
%e {1},
%e {1, 1},
%e {1, 2, 1},
%e {1, 5, 4, 1},
%e {1, 13, 17, 7, 1},
%e {1, 39, 75, 45, 11, 1},
%e {1, 151, 364, 290, 100, 16, 1},
%e {1, 783, 2065, 1974, 875, 196, 22, 1},
%e {1, 5167, 14034, 14833, 7819, 2226, 350, 29, 1},
%e {1, 40575, 112609, 125894, 74235, 25095, 4998, 582, 37, 1},
%e {1, 363391, 1035906, 1206805, 766205, 292152, 69153, 10200, 915, 46, 1}
%t p[x_, n_] = (If[n == 0, 0, Sum[StirlingS2[ n, m]*x^m, {m, 0, n}]/x] + Sum[Abs[StirlingS1[n, m]]*x^m, {m, 0, n}]);
%t Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}];
%t Flatten[%]
%o (PARI) T(n,k) = stirling(n,k+1,2) + abs(stirling(n,k,1)) \\ _Andrew Howroyd_, Jan 09 2024
%K nonn,tabl
%O 0,5
%A _Roger L. Bagula_, Dec 15 2008
%E Name clarified by _Andrew Howroyd_, Jan 09 2024