A127745 Counts Bell numbers (except for Catalans) associated with the partition number [n].

0, 0, 0, 1, 8, 50, 294, 1717, 10194, 62284, 394346, 2597266, 17827166, 127575414, 951411752, 7386583917, 59623674472, 499648882838, 4340548090590, 39033489125836, 362871600781796, 3482858492844510, 34471940635650958, 351444263328831458

Offset: 1

Author

Alford Arnold, Feb 25 2007

Keywords

• nonn
• uned

Comments

A074664 counts the Bell Numbers associated with the partition number [n]. A000108 counts the corresponding Catalan numbers and here we count the remaining Bell numbers associated with the partition number [n].

Examples

			There are 15 Bell objects when n = 4, 14 are also Catalans so a(4) = 1.
There are 52 Bell objects when n = 5, 42 are also Catalans; we know that 5 = 4+1 = 1+4 which accounts for two of the non-Catalan Bells so, a(5) = 52 - 42 - 2 = 8.
		

Crossrefs

Cf. A000041, A000108, A000110, A001399, A016098, A035300, A127743, A074664.

Formula

a(n) = A074664(n) - A000108(n-1)