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URL: https://oeis.org/A006541

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A006541
Number of dissimilarity relations on an n-set.
3
1, 1, 13, 4683, 102247563, 230283190977853, 81124824998504073881821, 6297562064950066033518373935334635, 144199280951655469628360978109406917583513090155, 1255482482235481041484313695469155949742941807533901307975355741
OFFSET
1,3
REFERENCES
M. Schader, Hierarchical analysis: classification with ordinal object dissimilarities, Metrika, 27 (1980), 127-132.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
M. Schader, Hierarchical analysis: classification with ordinal object dissimilarities, Metrika, 27 (1980), 127-132. [Annotated scanned copy]
M. Schader, Letter to N. J. A. Sloane, Aug 25 1981.
FORMULA
a(n) = Sum_{i=0..m} (m-i)!*Stirling2(m, m-i), where m = n*(n-1)/2.
a(n) = A000670(n*(n-1)/2).
MAPLE
b:= proc(n, k) b(n, k):= `if`(n=0, k!, k*b(n-1, k)+b(n-1, k+1)) end:
a:= n-> b(n*(n-1)/2, 0):
seq(a(n), n=1..12); # Alois P. Heinz, Dec 02 2024
MATHEMATICA
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 *)
PROG
(PARI) a(n)=ceil(polylog(-n*(n-1)/2, 1/2)/2) \\ Charles R Greathouse IV, Aug 27 2014
CROSSREFS
Sequence in context: A203676 A023345 A249941 * A189647 A185674 A103857
KEYWORD
nonn,nice,easy
EXTENSIONS
More terms from James Sellers, Jan 19 2000
STATUS
approved