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A245408
Number of endofunctions on [n] such that no element has a preimage of cardinality four.
2
1, 1, 4, 27, 252, 3025, 44406, 770623, 15434616, 350420337, 8893045900, 249474767861, 7665670072116, 256045368531433, 9237038259841770, 357934480164387225, 14827066792663179616, 653843231295154192017, 30581468519362170893784, 1512123060477719223218791
OFFSET
0,3
LINKS
FORMULA
a(n) = n! * [x^n] (exp(x)-x^4/4!)^n.
MAPLE
b:= proc(n, i) option remember; `if`(n=0 and i=0, 1, `if`(i<1, 0,
add(`if`(j=4, 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^4/4!)^n, {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 23 2014 *)
CROSSREFS
Column k=4 of A245405.
Sequence in context: A239371 A201996 A239368 * A243696 A158836 A350276
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 21 2014
STATUS
approved