A169587 The total number of ways of partitioning the multiset {1,1,1,2,3,...,n-2}.

3, 7, 21, 74, 296, 1315, 6393, 33645, 190085, 1145246, 7318338, 49376293, 350384315, 2606467211, 20266981269, 164306340566, 1385709542808, 12133083103491, 110095025916745, 1033601910417425, 10024991744613469, 100316367530768074, 1034373400144455266

Offset

3,1

Links

Alois P. Heinz, Table of n, a(n) for n = 3..576

M. Griffiths, I. Mezo, A generalization of Stirling Numbers of the Second Kind via a special multiset, JIS 13 (2010) #10.2.5.

M. Griffiths, Generalized Near-Bell Numbers, JIS 12 (2009) 09.5.7

Formula

For n>=3, a(n)=(Bell(n)+3Bell(n-1)+5Bell(n-2)+2Bell(n-3))/6, where Bell(n) is the n-th Bell number (the Bell numbers are given in A000110).

E.g.f.: (e^(3x)+6e^(2x)+9e^x+2)(e^(e^x-1))/6.

Example

The partitions of {1,1,1,2} are {{1},{1},{1},{2}}, {{1,1},{1},{2}}, {{1,2},{1},{1}}, {{1,1},{1,2}}, {{1,1,1},{2}}, {{1,1,2},{1}} and {{1,1,1,2}}, so a(4)=7.

Mathematica

Table[(BellB[n] + 3 BellB[n - 1] + 5 BellB[n - 2] + 2 BellB[n - 3])/ 6, {n, 3, 23}]

Crossrefs

This is related to A000110, A035098 and A169588.

Row n=3 of A346426.

Cf. A346813.

Sequence in context: A148679 A148680 A001576 * A075211 A075212 A319123

Adjacent sequences: A169584 A169585 A169586 * A169588 A169589 A169590

Keyword

nonn

Author

Martin Griffiths, Dec 02 2009

Status

approved