A006541 Number of dissimilarity relations on an n-set.

1, 1, 13, 4683, 102247563, 230283190977853, 81124824998504073881821, 6297562064950066033518373935334635, 144199280951655469628360978109406917583513090155, 1255482482235481041484313695469155949742941807533901307975355741

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• easy

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

• Vincenzo Librandi, Table of n, a(n) for n = 1..29
• 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.

Crossrefs

Cf. A000670, A005121.

Programs

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 *)

PARI

a(n)=ceil(polylog(-n*(n-1)/2, 1/2)/2) \\ Charles R Greathouse IV, Aug 27 2014

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).

Extensions

More terms from James Sellers, Jan 19 2000