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A241580
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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.
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3
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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
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OFFSET
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1,4
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=1..45.
R. K. Guy, Letter to N. J. A. Sloane, Jun 21, 1975
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EXAMPLE
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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;
...
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MAPLE
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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:
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CROSSREFS
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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
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KEYWORD
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nonn,tabl
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AUTHOR
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N. J. A. Sloane, Apr 29 2014
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STATUS
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approved
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