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A245406 Number of endofunctions on [n] such that no element has a preimage of cardinality two. 3
1, 1, 2, 9, 76, 825, 10206, 143521, 2313200, 42482313, 875799550, 19972186311, 498430219464, 13509979971241, 395352049852046, 12425644029361725, 417456939168255616, 14929305882415781265, 566234625018001351230, 22701936510037394021395, 959341639105178919209000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..396 (first 200 terms from Alois P. Heinz)

FORMULA

a(n) = n! * [x^n] (exp(x)-x^2/2!)^n.

a(n) ~ c * d^n * n^n / exp(n), where d = 2.166383277092734585444028653747119..., c = 0.8627963719760750933657356839596... . - Vaclav Kotesovec, Jul 24 2014

MAPLE

b:= proc(n, i) option remember; `if`(n=0 and i=0, 1, `if`(i<1, 0,

       add(`if`(j=2, 0, b(n-j, i-1) *binomial(n, j)), j=0..n)))

    end:

a:= n-> b(n$2):

seq(a(n), n=0..25);

MATHEMATICA

Table[n!*SeriesCoefficient[(E^x - x^2/2)^n, {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 23 2014 *)

With[{k=2}, Flatten[{1, Table[Sum[Binomial[n, j]*Binomial[n, k*j]*(-1)^j*(n-j)^(n-k*j)*(k*j)!/(k!)^j, {j, 0, n/k}], {n, 1, 20}]}]]  (* Vaclav Kotesovec, Jul 24 2014 *)

CROSSREFS

Column k=2 of A245405.

Cf. A245493.

Sequence in context: A232471 A277181 A105785 * A276742 A123680 A132621

Adjacent sequences:  A245403 A245404 A245405 * A245407 A245408 A245409

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 21 2014

STATUS

approved

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Last modified September 15 18:22 EDT 2019. Contains 327082 sequences. (Running on oeis4.)