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A065440 a(n) = (n-1)^n. 12
1, 0, 1, 8, 81, 1024, 15625, 279936, 5764801, 134217728, 3486784401, 100000000000, 3138428376721, 106993205379072, 3937376385699289, 155568095557812224, 6568408355712890625, 295147905179352825856 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

a(n) is the number of functions from {1,2,...,n} into {1,2,...,n} that have no fixed points.

The probability that a random function from {1,2,...,n} into {1,2,...,n} has no fixed point is equal to a(n)/n^n; it tends to 1/e when n tends to infinity. - Robert FERREOL, Mar 29 2017

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..100

Mustafa Obaid et al., The number of complete exceptional sequences for a Dynkin algebra, arXiv preprint arXiv:1307.7573 [math.RT], 2013.

FORMULA

a(n) = A007778(n-1).

E.g.f.: x/(T(x)*(1-T(x))) (where T(x) is Euler's tree function, the E.g.f. for n^(n-1)) (see A000169).

a(n) = Sum_{k=0..n} (-1)^k*binomial(n,k)*n^(n-k). - Robert FERREOL, Mar 28 2017

MATHEMATICA

Table[(n-1)^n, {n, 0, 20}] (* Harvey P. Dale, Jan 03 2015 *)

PROG

(PARI) { for (n=0, 100, write("b065440.txt", n, " ", (n - 1)^n) ) } \\ Harry J. Smith, Oct 19 2009

CROSSREFS

Essentially the same as A007778 - note T(x) = -W(-x)).

Column k=0 of A055134.

Cf. A284458.

Sequence in context: A207994 A210127 A007778 * A318047 A092366 A022519

Adjacent sequences:  A065437 A065438 A065439 * A065441 A065442 A065443

KEYWORD

nonn,easy

AUTHOR

Len Smiley, Nov 17 2001

STATUS

approved

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Last modified March 30 16:16 EDT 2020. Contains 333127 sequences. (Running on oeis4.)