A322883 Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals ten.

0, 1, 515, 22253, 430909, 6094476, 74507486, 847129333, 9296465127, 100540964675, 1085004090887, 11775039127122, 129155075413877, 1436488582202316, 16235344928131625, 186710546094489052, 2186538096666720967, 26085011069325363939, 317049671003606985326

Offset

10,3

Links

Alois P. Heinz, Table of n, a(n) for n = 10..579

Wikipedia, Partition of a set

Formula

a(n) = A287260(n) - A287259(n).

Maple

b:= proc(n, k, m, l) option remember; `if`(n<1, 1,
     `if`(l-n>k, 0, b(n-1, k, m+1, n))+m*b(n-1, k, m, l))
    end:
A:= (n, k)-> b(n-1, min(k, n-1), 1, n):
a:= n-> (k-> A(n, k)-A(n, k-1))(10):
seq(a(n), n=10..30);

Crossrefs

Column k=10 of A287215.

Cf. A287259, A287260.

Sequence in context: A246244 A257087 A254643 * A332151 A234826 A232574

Adjacent sequences: A322880 A322881 A322882 * A322884 A322885 A322886

Keyword

nonn

Author

Alois P. Heinz, Dec 29 2018

Status

approved