

A281912


Number of sequences of balls colored with at most n colors such that exactly one ball is of a color seen earlier in the sequence.


3



1, 8, 57, 424, 3425, 30336, 294553, 3123632, 36003969, 448816600, 6022033721, 86587079448, 1328753602657, 21683227579664, 375013198304025, 6853321766162656, 131976208783240193, 2671430511854158632, 56709161712552286009, 1259836187316759240200
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OFFSET

1,2


COMMENTS

Note that any such sequence has at least 2 balls, and at most n+1
Number of sequences of balls colored with at most n colors such that exactly two balls are the same color as some other ball in the sequence (necessarily each other).  Jeremy Dover, Sep 26 2017


LINKS



FORMULA

a(n) = n! * Sum_{k=2..n+1} binomial(k,2)/(n+1k)!.
a(n) = n if n < 2, a(n) = n*((n+2)/(n1)*a(n1)  a(n2)) for n >= 2.  Alois P. Heinz, Feb 02 2017


EXAMPLE

n=1 => AA > a(1) = 1.
n=2 => AA,BB,AAB,ABA,BAA,BBA,BAB,ABB > a(2) = 8.


MAPLE

a:= proc(n) option remember;
`if`(n<2, 1, a(n1)*(n+2)/(n1)a(n2))*n
end:


MATHEMATICA

Table[n!*Sum[Binomial[k, 2]/(n + 1  k)!, {k, 2, n + 1}], {n, 20}] (* Michael De Vlieger, Feb 02 2017 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



