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 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. 3
 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 (list; table; graph; refs; listen; history; text; internal format)
 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 R. K. Guy, Letter to N. J. A. Sloane, Jun 21, 1975 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 T(n,0) is A231797, row sums are A241581. Sequence in context: A223537 A140860 A019681 * A323257 A054529 A074934 Adjacent sequences: A241577 A241578 A241579 * A241581 A241582 A241583 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, Apr 29 2014 STATUS approved

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Last modified March 29 22:15 EDT 2023. Contains 361599 sequences. (Running on oeis4.)