A006541 - OEIS

%I M4920 #33 Dec 02 2024 14:43:39

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

%T 6297562064950066033518373935334635,

%U 144199280951655469628360978109406917583513090155,1255482482235481041484313695469155949742941807533901307975355741

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

%F a(n) = A000670(n*(n-1)/2).

%p b:= proc(n, k) b(n, k):= `if`(n=0, k!, k*b(n-1, k)+b(n-1, k+1)) end:

%p a:= n-> b(n*(n-1)/2, 0):

%p seq(a(n), n=1..12);  # _Alois P. Heinz_, Dec 02 2024

%t a[n_] := PolyLog[-n(n-1)/2, 1/2]/2; a[1]=1; Table[a[n], {n, 1, 9}] (* _Jean-François 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. A000670, A005121.

%K nonn,nice,easy

%O 1,3

%A _N. J. A. Sloane_

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