A005646 Number of classifications of n elements.

1, 1, 1, 3, 6, 26, 122, 1015, 11847, 208914, 5236991, 184321511

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• more

Comments

"A 'classification' is a set of n type-specimens each one of which is corralled on its own by the union of a set of binary partitions, none of which could be omitted without leaving 2 types unseparated".

From Robert Munafo, Jan 24 2010: (Start)

Extensive explanation with illustrations on Munafo web page.

This sequence gives the row sums of triangle A171871. (End)

Examples

			Illustrated examples on Munafo web page. - _Robert Munafo_, Jan 24 2010
		

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
• P. J. Wexler, On the number of taxonomies; or the odds on 'structuralism', American Anthropologist, 73 (1971), 1258.

Links

• Robert Munafo, Web page about this sequence (with additional terms) [Added Jan 04 2010]
• P. J. Wexler and D. H. Fremlin, The number of classifications of up to seven classificanda, Classification Society Bull., 4 (No. 3, 1979), 2-4. (Annotated scanned copy)

Crossrefs

Cf. A000055, A171872, A171873. - Robert Munafo, Jan 24 2010

Extensions

1015 term first calculated by Andrew Weimholt, Dec 15 2009

11847 term first calculated by Andrew Weimholt, Dec 19 2009

208914 term first calculated by Robert Munafo, Dec 29 2009

5236990 term (erroneous) from Robert Munafo, Dec 30 2009

Erroneous "5236990" corrected to 5236991 by Robert Munafo, Jan 01 2010

184321511 term first calculated by Robert Munafo, Jan 10 2010