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A241579 Square array read by antidiagonals downwards: T(n,k) = Sum_{j=1..k} n^(k-j)*Stirling_2(k,j) (n >= 0, k >= 1).

%I A241579 #15 Jun 30 2023 03:48:18
%S A241579 1,1,1,1,2,1,1,5,3,1,1,15,11,4,1,1,52,49,19,5,1,1,203,257,109,29,6,1,
%T A241579 1,877,1539,742,201,41,7,1,1,4140,10299,5815,1657,331,55,8,1,1,21147,
%U A241579 75905,51193,15821,3176,505,71,9,1,1,115975,609441,498118,170389,35451,5497,729,89,10,1
%N A241579 Square array read by antidiagonals downwards: T(n,k) = Sum_{j=1..k} n^(k-j)*Stirling_2(k,j) (n >= 0, k >= 1).
%H A241579 A. Kerber, <a href="https://doi.org/10.1016/0012-365X(78)90163-2">A matrix of combinatorial numbers related to the symmetric groups</a>, Discrete Math., 21 (1978), 319-321.
%H A241579 A. Kerber, <a href="/A004211/a004211.pdf">A matrix of combinatorial numbers related to the symmetric groups</a>, Discrete Math., 21 (1978), 319-321. [Annotated scanned copy]
%e A241579 Array begins:
%e A241579 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A241579 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, ...
%e A241579 1, 3, 11, 49, 257, 1539, 10299, 75905, 609441, 5284451, 49134923, 487026929, ...
%e A241579 1, 4, 19, 109, 742, 5815, 51193, 498118, 5296321, 60987817, 754940848, 9983845261, ...
%e A241579 1, 5, 29, 201, 1657, 15821, 170389, 2032785, 26546673, 376085653, 5736591885, 93614616409, ...
%e A241579 1, 6, 41, 331, 3176, 35451, 447981, 6282416, 96546231, 1611270851, 28985293526, 558413253581, ...
%e A241579 1, 7, 55, 505, 5497, 69823, 1007407, 16157905, 284214097, 5432922775, 112034017735, 2476196276617, ...
%e A241579 1, 8, 71, 729, 8842, 125399, 2026249, 36458010, 719866701, 15453821461, 358100141148, 8899677678109, ...
%e A241579 ...
%p A241579 with(combinat):
%p A241579 T:=(n,k)->add(n^(k-j)*stirling2(k,j),j=1..k);
%p A241579 r:=n->[seq(T(n,k),k=1..12)];
%p A241579 for n from 0 to 8 do lprint(r(n)); od:
%Y A241579 Three versions of this array are A111673, A241578, A241579.
%Y A241579 Rows and columns give A000110, A004211, A004212, A004213, A005011, A005012, A028387, A241577.
%K A241579 nonn,tabl
%O A241579 0,5
%A A241579 _N. J. A. Sloane_, Apr 29 2014