A169588 The total number of ways of partitioning the multiset {1,1,1,1,2,3,...,n-3}.

5, 12, 38, 141, 592, 2752, 13960, 76464, 448603, 2801054, 18516832, 129034659, 944356507, 7235605732, 57879020756, 482189616711, 4174720731316, 37489711726834, 348592657600818, 3350919079643612, 33252861484374737, 340209759518479300, 3584240435109146792

Offset: 4

Author

Martin Griffiths, Dec 02 2009

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..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

Crossrefs

This is related to A000110, A035098 and A169587.

Row n=4 of A346426.

Cf. A346814.

Programs

Mathematica

Table[(BellB[n] + 6 BellB[n - 1] + 17 BellB[n - 2] + 20 BellB[n - 3] + 21 BellB[n - 4])/24, {n, 4, 23}]

Formula

For n>=4, a(n)=(Bell(n)+6Bell(n-1)+17Bell(n-2)+20Bell(n-3)+21Bell(n-4))/24, where Bell(n) is the n-th Bell number (the Bell numbers are given in A000110). e.g.f. (e^(4x)+12e^(3x)+42e^(2x)+44e^x+21)(e^(e^x-1))/24.