OFFSET
1,4
COMMENTS
Arises in analysis of game with n players: each person picks a number from 1 to n, and the winner is the largest unique choice (see Guy's letter). T(n,k) is the number out of all possible games (i.e., all n^n sets of choices) which are won by a given player who has chosen k.
LINKS
EXAMPLE
Triangle begins:
1;
0, 1;
2, 2, 4;
3, 9, 15, 27;
40, 52, 88, 148, 256;
205, 405, 665, 1105, 1845, 3125;
2556, 3786, 6216, 10206, 16836, 27906, 46656;
24409, 42301, 68803, 112315, 183757, 301609, 496951, 823543;
...
MAPLE
M:=20;
M2:=10;
T[1, 1]:=1:
for n from 2 to M do
T[n, n]:=(n-1)^(n-1);
for k from n-1 by -1 to 1 do
T[n, k]:=T[n, k+1]-(n-1)*T[n-1, k]:
od:
od:
for n from 1 to M2 do lprint([seq(T[n, k], k=1..n)]); od:
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Apr 29 2014
STATUS
approved