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A245411
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Number of endofunctions on [n] such that no element has a preimage of cardinality seven.
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2
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1, 1, 4, 27, 256, 3125, 46656, 823536, 16776768, 387399753, 9999125200, 285275370611, 8914569819552, 302808495261181, 11108991885125512, 437751439912499175, 18439707410896028416, 826876746821203814161, 39326776141693679404128, 1977312147376328609765419
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = n! * [x^n] (exp(x)-x^7/7!)^n.
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MAPLE
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b:= proc(n, i) option remember; `if`(n=0 and i=0, 1,
`if`(i<1, 0, add(`if`(j=7, 0, b(n-j, i-1)*
binomial(n, j)), j=0..n)))
end:
a:= n-> b(n$2):
seq(a(n), n=0..25);
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MATHEMATICA
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Table[n!*SeriesCoefficient[(E^x-x^7/7!)^n, {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 23 2014 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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