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A066320 Triangle read by rows: T(n, k) = binomial(n, k)*k^k*(n-k)^(n-k-1) k=0..n-1.

%I A066320 #16 Jan 12 2024 11:56:39
%S A066320 1,2,2,9,6,12,64,36,48,108,625,320,360,540,1280,7776,3750,3840,4860,
%T A066320 7680,18750,117649,54432,52500,60480,80640,131250,326592,2097152,
%U A066320 941192,870912,945000,1146880,1575000,2612736,6588344,43046721
%N A066320 Triangle read by rows: T(n, k) = binomial(n, k)*k^k*(n-k)^(n-k-1) k=0..n-1.
%D A066320 F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 68 (2.1.43).
%F A066320 E.g.f.: -LambertW(-y)/(1+LambertW(-x*y)). - _Vladeta Jovovic_, Jan 26 2006
%F A066320 T(n, k) = n*binomial(n-1, k-1)*(k-1)^(k-1)*(n-k+1)^(n-k-1) assuming offset (1, 1). - _Peter Luschny_, Jan 12 2024
%e A066320 Triangle starts:
%e A066320   [1][      1]
%e A066320   [2][      2,      2]
%e A066320   [3][      9,      6,     12]
%e A066320   [4][     64,     36,     48,    108]
%e A066320   [5][    625,    320,    360,    540,    1280]
%e A066320   [6][   7776,   3750,   3840,   4860,    7680,   18750]
%e A066320   [7][ 117649,  54432,  52500,  60480,   80640,  131250,  326592]
%e A066320   [8][2097152, 941192, 870912, 945000, 1146880, 1575000, 2612736, 6588344]
%o A066320 (Julia) # Assuming offset (n=1, k=1).
%o A066320 T(n, k) = binomial(n-1, k-1)*(k-1)^(k-1)*n*(n-k+1)^(n-k-1)
%o A066320 for n in 1:9 (println([n], [T(n, k) for k in 1:n])) end
%o A066320 # _Peter Luschny_, Jan 12 2024
%Y A066320 T = n * A185390 after proper alignment of offsets.
%Y A066320 Columns 1, 2: A000169, A055541.
%Y A066320 Main diagonal: A055897.
%Y A066320 Row sums give A000312.
%K A066320 nonn,tabl
%O A066320 1,2
%A A066320 _Christian G. Bower_, Dec 13 2001