A322879 Number of set partitions of [n] such that the maximal absolute difference between the least elements of consecutive blocks equals six.

0, 1, 35, 413, 3709, 30396, 242366, 1934021, 15653524, 129267234, 1091892025, 9444993005, 83722879838, 760771479660, 7087056828919, 67674638461955, 662248199987728, 6638947646238102, 68153572265860585, 716151632403862252, 7699437833837232406

Offset

6,3

Links

Alois P. Heinz, Table of n, a(n) for n = 6..581

Wikipedia, Partition of a set

Formula

a(n) = A287256(n) - A287255(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))(6):
seq(a(n), n=6..30);

Crossrefs

Column k=6 of A287215.

Cf. A287255, A287256.

Sequence in context: A238539 A075664 A133317 * A105947 A183846 A219936

Adjacent sequences: A322876 A322877 A322878 * A322880 A322881 A322882

Keyword

nonn

Author

Alois P. Heinz, Dec 29 2018

Status

approved