%I #4 Mar 30 2012 17:36:01

%S 1,2,4,9,12,27,64,72,108,256,625,640,810,1280,3125,7776,7500,8640,

%T 11520,18750,46656,117649,108864,118125,143360,196875,326592,823543,

%U 2097152,1882384,1959552,2240000,2800000,3919104,6588344,16777216,43046721

%N Triangle read by rows: T(n,k)=binomial(n,k-1)*k^(k-1)*(n+1-k)^(n-k) (1<=k<=n).

%D I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983,(p.27, Problem 1.2.6 (b)).

%F T(n, k)=binomial(n, k-1)*k^(k-1)*(n+1-k)^(n-k) (1<=k<=n).

%p T:=proc(n,k) if k<=n then binomial(n,k-1)*k^(k-1)*(n+1-k)^(n-k) else 0 fi end: for n from 1 to 9 do seq(T(n,k),k=1..n) od; # yields sequence in triangular form

%Y Row sums yield A053506. T(n, 1)=A000169(n). T(n, n)=A000312(n).

%K nonn,tabl

%O 1,2

%A _Emeric Deutsch_, Mar 27 2005