A377058 Triangle of generalized Stirling numbers of the lower level of the hierarchy (case m=2).
1, 5, 1, 32, 11, 1, 248, 113, 18, 1, 2248, 1230, 263, 26, 1, 23272, 14534, 3765, 505, 35, 1, 270400, 186992, 55654, 9115, 865, 45, 1, 3479744, 2612000, 865186, 163779, 19110, 1372, 56, 1, 49079936, 39434448, 14235388, 3013164, 408569, 36288, 2058, 68, 1
Offset: 0
Keywords
Examples
[0] 1; [1] 5, 1; [2] 32, 11, 1; [3] 248, 113, 18, 1; [4] 2248, 1230, 263, 26, 1; [5] 23272, 14534, 3765, 505, 35, 1; [6] 270400, 186992, 55654, 9115, 865, 45, 1; [7] 3479744, 2612000, 865186, 163779, 19110, 1372, 56, 1; [8] 49079936, 39434448, 14235388, 3013164, 408569, 36288, 2058, 68, 1;
Links
- Igor Victorovich Statsenko, Relationships of "P"-generalized Stirling numbers of the first kind with other generalized Stirling numbers, Innovation science No 10-1, State Ufa, Aeterna Publishing House, 2024, pp. 19-22. In Russian.
Programs
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Maple
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);
Formula
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.
Comments