6,8

The number of partitions of the set N, |N|=n, into k blocks, all of cardinality greater than or equal to 6. This is the 6-associated Stirling number of the second kind.

This is entered as a triangular array. The entries S_6(n,k) are zero for 6k>n, so these values are omitted. Initial entry in sequence is S_6(6,1).

Rows are of lengths 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, ...

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 222.

A. E. Fekete, Apropos two notes on notation, Amer. Math. Monthly, 101 (1994), 771-778.

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 76.

S_r(n+1, k)=k S_r(n, k)+binomial(n, r-1)S_r(n-r+1, k-1) for this sequence, r=6 G.f.: sum(S_r(n, k)u^k ((t^n)/(n!)), n=0..infty, k=0..infty)=exp(u(e^t-sum(t^i/i!, i=0..r-1)))

There are 462 ways of partitioning a set N of cardinality 12 into 2 blocks each of cardinality at least 6, so S_6(12,2)=462.

Cf. A008299, A059022, A059023, A059024.

Sequence in context: A138956 A107121 A101734 this_sequence A094380 A104397 A108749

Adjacent sequences: A059022 A059023 A059024 this_sequence A059026 A059027 A059028

nonn,tabf,nice

Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Dec 14 2000 # Extensions to existing sequences