



0, 1, 12, 156, 2360, 41400, 831012, 18832576, 476200944, 13301078400, 406907517500, 13534968927744, 486470108273448, 18790567023993856, 776343673316956500, 34165751933338828800, 1595693034061797583328, 78831769938218360930304
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OFFSET

0,3


COMMENTS

This is Sum_{all n^(n2) labeled trees T on n nodes} Sum_{1<=i<j<=n} distance(node i, node j).
a(n) is the total number of all defects in defective parking functions of length n+1.  Alois P. Heinz, Nov 28 2015
With offset 1, a(n) is the number of unordered pairs {f,g} where for some nonempty proper subset S of [n], f:S>S and g:[n]\S>[n]\S.  Geoffrey Critzer, Apr 23 2017


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..380
J. Riordan and N. J. A. Sloane, Enumeration of rooted trees by total height, J. Austral. Math. Soc., vol. 10 pp. 278282, 1969.
Peter Winkler, Mean distance in a tree, in Computational algorithms, operations research and computer science (Burnaby, BC, 1987). Discrete Appl. Math. 27 (1990), no. 12, 179185. [For background information only.]


FORMULA

a(n) = Sum_{k>0} k * A264902(n+1,k).  Alois P. Heinz, Nov 28 2015


MATHEMATICA

Table[Sum[Binomial[n, k] (n  k)^(n  k) k^k, {k, n  1}]/2, {n, 18}] (* Michael De Vlieger, Apr 24 2017, after Harvey P. Dale at A001864 *)


CROSSREFS

Cf. A001864, A264902.
Sequence in context: A158546 A110216 A218839 * A003130 A015000 A220225
Adjacent sequences: A036273 A036274 A036275 * A036277 A036278 A036279


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane.


STATUS

approved



