1,5

A000041 counts numeric partitions. A001399 counts numeric partitions such that no part is greater than three and A035300 counts the remaining numeric partitions. A000110 counts the Bell numbers A000108 counts the Catalan numbers (which are a subset of the Bells). SeQ A016098 counts the remaining Bell numbers. A074664 counts the Bell Numbers associated with the partition number [n]. A000108 counts the corresponding Catalan numbers and A127745 counts the remaining Bell numbers associated with the partition number [n]. The sequences begin A074664(n) = 1 1 2 6 22 92 426 2146 11624 ... A000108(n) = 1 1 2 5 14 42 132 429 1430 ... A127745(n) = 0 0 0 1 8 50 294 1717 10194 ...

A127745(n) = A074664(n) - A000108(n)

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

a(5) = 8

Cf. A000041 A000108 A000110 A001399 A016098 A035300 A127743 A074664.

Sequence in context: A081180 A052177 A115598 this_sequence A037547 A061801 A133129

Adjacent sequences: A127742 A127743 A127744 this_sequence A127746 A127747 A127748

nonn,uned

Alford Arnold (Alford1940(AT)aol.com), Feb 25 2007