A103690 Triangle read by rows: T(n,k)=binomial(n,k-1)*k^(k-1)*(n+1-k)^(n-k) (1<=k<=n).

1, 2, 4, 9, 12, 27, 64, 72, 108, 256, 625, 640, 810, 1280, 3125, 7776, 7500, 8640, 11520, 18750, 46656, 117649, 108864, 118125, 143360, 196875, 326592, 823543, 2097152, 1882384, 1959552, 2240000, 2800000, 3919104, 6588344, 16777216, 43046721

Offset: 1

Author

Emeric Deutsch, Mar 27 2005

Keywords

• nonn
• tabl

References

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

Crossrefs

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

Programs

Maple

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

Formula

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