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 A377058 #11 Oct 17 2024 18:50:43
%S A377058 1,5,1,32,11,1,248,113,18,1,2248,1230,263,26,1,23272,14534,3765,505,
%T A377058 35,1,270400,186992,55654,9115,865,45,1,3479744,2612000,865186,163779,
%U A377058 19110,1372,56,1,49079936,39434448,14235388,3013164,408569,36288,2058,68,1
%N A377058 Triangle of generalized Stirling numbers of the lower level of the hierarchy (case m=2).
%C A377058 These numbers are a subset of the generalized Stirling numbers introduced in A370518. Therefore, we assume them to be numbers of the lower level of hierarchy with respect to A370518.
%H A377058 Igor Victorovich Statsenko, <a href="https://aeterna-ufa.ru/sbornik/IN-2024-10-1.pdf#page=19">Relationships of "P"-generalized Stirling numbers of the first kind with other generalized Stirling numbers</a>, Innovation science No 10-1, State Ufa, Aeterna Publishing House, 2024, pp. 19-22. In Russian.
%F A377058 T(m, n, k) = Sum_{i=0..n} Sum_{j=i..n} Stirling1(n-j, k)*binomial(n+m, i)*binomial(n, j)* binomial(j, i)*i!*m^(j-i), for m = 2.
%e A377058 [0] 1;
%e A377058 [1] 5, 1;
%e A377058 [2] 32, 11, 1;
%e A377058 [3] 248, 113, 18, 1;
%e A377058 [4] 2248, 1230, 263, 26, 1;
%e A377058 [5] 23272, 14534, 3765, 505, 35, 1;
%e A377058 [6] 270400, 186992, 55654, 9115, 865, 45, 1;
%e A377058 [7] 3479744, 2612000, 865186, 163779, 19110, 1372, 56, 1;
%e A377058 [8] 49079936, 39434448, 14235388, 3013164, 408569, 36288, 2058, 68, 1;
%p A377058 T := (m,n,k) -> add(add(Stirling1(n-j,k)*binomial(n+m,i)*binomial(n,j)*binomial(j,i)*i!*m^(j-i), j=i..n), i=0..n): m:=2: seq(seq(T(m,n,k), k=0..n), n=0..10);
%Y A377058 A361649 (row sums).
%Y A377058 Triangle for m=0: A130534.
%Y A377058 Triangle for m=1: A376863.
%K A377058 nonn
%O A377058 0,2
%A A377058 _Igor Victorovich Statsenko_, Oct 14 2024