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Binomial(n,2)*B(n-1)*(B(n)-B(n-1)), where B() = A000110() are the Bell numbers.
2

%I #22 Apr 17 2015 14:37:34

%S 0,0,1,18,300,5550,117780,2873262,80126228,2534723280,90239747220,

%T 3588582531875,158318375911740,7700793136255440,410691133882551795,

%U 23894146232727414630,1509723335738373490800,103169903975944947302744,7597003720932150826636260,600748548233457344454385722

%N Binomial(n,2)*B(n-1)*(B(n)-B(n-1)), where B() = A000110() are the Bell numbers.

%C Sum of the Rand distance over all unordered pairs of partitions.

%H Frank Ruskey and Jennifer Woodcock, <a href="http://dx.doi.org/10.1007/978-3-642-25011-8_23">The Rand and block distances of pairs of set partitions</a>, Combinatorial algorithms, 287-299, Lecture Notes in Comput. Sci., 7056, Springer, Heidelberg, 2011.

%t Table[Binomial[n, 2]*BellB[n - 1] (BellB[n] - BellB[n - 1]), {n, 19}] (* _Michael De Vlieger_, Apr 16 2015 *)

%Y Cf. A000110, A191200.

%Y Equals half A124104.

%K nonn

%O 0,4

%A _N. J. A. Sloane_, Aug 26 2011