A376634 Triangle read by rows: T(n, k) = Sum_{i=0..n-k} Stirling1(i + m, m)*binomial(n+m+1, n-k-i)*(n + m - k)!/(i + m)!, for m = 2.
1, 9, 1, 71, 12, 1, 580, 119, 15, 1, 5104, 1175, 179, 18, 1, 48860, 12154, 2070, 251, 21, 1, 509004, 133938, 24574, 3325, 335, 24, 1, 5753736, 1580508, 305956, 44524, 5000, 431, 27, 1, 70290936, 19978308, 4028156, 617624, 74524, 7155, 539, 30, 1, 924118272, 270074016, 56231712, 8969148, 1139292, 117454, 9850, 659, 33, 1, 13020978816, 3894932448, 832391136, 136954044, 18083484, 1961470, 176554, 13145, 791, 36, 1
Offset: 0
Examples
Triangle starts: [0] 1; [1] 9, 1; [2] 71, 12, 1; [3] 580, 119, 15, 1; [4] 5104, 1175, 179, 18, 1; [5] 48860, 12154, 2070, 251, 21, 1; [6] 509004, 133938, 24574, 3325, 335, 24, 1; [7] 5753736, 1580508, 305956, 44524, 5000, 431, 27, 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.
Crossrefs
Programs
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Maple
T:=(m,n,k)->add(Stirling1(i+m,m)*binomial(n+m+1,n-k-i)*(n+m-k)!/(i+m)!,i=0..n-k):m:=2:seq(seq(T(m,n,k), k=0..n),n=0..10);
Comments