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A006541 Number of dissimilarity relations on an n-set.
(Formerly M4920)
2

%I M4920

%S 1,1,13,4683,102247563,230283190977853,81124824998504073881821,

%T 6297562064950066033518373935334635,

%U 144199280951655469628360978109406917583513090155

%N Number of dissimilarity relations on an n-set.

%D M. Schader, Hierarchical analysis: classification with ordinal object dissimilarities, Metrika, 27 (1980), 127-132.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Vincenzo Librandi, <a href="/A006541/b006541.txt">Table of n, a(n) for n = 1..29</a>

%H M. Schader, <a href="/A005121/a005121_1.pdf">Hierarchical analysis: classification with ordinal object dissimilarities</a>, Metrika, 27 (1980), 127-132. [Annotated scanned copy]

%H M. Schader, <a href="/A005121/a005121.pdf">Letter to N. J. A. Sloane</a>, Aug 25 1981.

%F Sum_{i=0..m-1} (m-i)!*Stirling2(m, m-i), where m = n(n-1)/2.

%t a[n_] := PolyLog[-n(n-1)/2, 1/2]/2; a[1]=1; Table[a[n], {n, 1, 9}] (* _Jean-Fran├žois Alcover_, Jun 28 2012, after _Wouter Meeussen_ *)

%o (PARI) a(n)=ceil(polylog(-n*(n-1)/2, 1/2)/2) \\ _Charles R Greathouse IV_, Aug 27 2014

%Y Cf. A005121.

%Y A000670(n(n-1)/2).

%K nonn,nice,easy

%O 1,3

%A _N. J. A. Sloane_

%E More terms from _James A. Sellers_, Jan 19 2000

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Last modified April 7 10:38 EDT 2020. Contains 333300 sequences. (Running on oeis4.)