A065440 a(n) = (n-1)^n.

1, 0, 1, 8, 81, 1024, 15625, 279936, 5764801, 134217728, 3486784401, 100000000000, 3138428376721, 106993205379072, 3937376385699289, 155568095557812224, 6568408355712890625, 295147905179352825856, 14063084452067724991009, 708235345355337676357632

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.

Row sums of A350452.

Cf. A284458.

Sequence in context: A207994 A210127 A007778 * A338694 A318047 A338685

Adjacent sequences: A065437 A065438 A065439 * A065441 A065442 A065443

Keyword

nonn,easy

Author

Len Smiley, Nov 17 2001

Status

approved