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A245410
Number of endofunctions on [n] such that no element has a preimage of cardinality six.
2
1, 1, 4, 27, 256, 3125, 46650, 823249, 16766240, 387033417, 9986221900, 284803470611, 8896457440872, 302075780925685, 11077712976422470, 436342859278138275, 18372866764869817216, 823539597176786793105, 39151767720093507173304, 1967688517596911564272795
OFFSET
0,3
LINKS
FORMULA
a(n) = n! * [x^n] (exp(x)-x^6/6!)^n.
MAPLE
b:= proc(n, i) option remember; `if`(n=0 and i=0, 1,
`if`(i<1, 0, add(`if`(j=6, 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^6/6!)^n, {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 23 2014 *)
CROSSREFS
Column k=6 of A245405.
Sequence in context: A245409 A190125 A324805 * A324806 A245411 A324807
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 21 2014
STATUS
approved