A241580 Triangle read by rows: T(n,k) (1 <= k <= n) defined by T(n,n) = (n-1)^(n-1), T(n,k) = T(n,k+1) - (n-1)*T(n-1,k) for k = n-1 .. 1.

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, 347712, 542984, 881392, 1431816, 2330336, 3800392, 6213264, 10188872, 16777216

Offset: 1

Author

N. J. A. Sloane, Apr 29 2014

Keywords

• nonn
• tabl

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.

Examples

			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;
  ...
		

Links

• R. K. Guy, Letter to N. J. A. Sloane, Jun 21, 1975

Crossrefs

T(n,0) is A231797, row sums are A241581.

Programs

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: