A320764 Number of ordered set partitions of [n] where the maximal block size equals eight.

1, 18, 360, 7260, 152460, 3361644, 78041964, 1908389340, 49118959890, 1328964080730, 37738620245898, 1122927974067042, 34953464391146730, 1136306352798186570, 38520124906043253330, 1359621561034260858906, 49896547074800880656202, 1901350452285623246965200

Offset: 8

Author

Alois P. Heinz, Oct 20 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..425

Crossrefs

Column k=8 of A276922.

Cf. A276927, A276928.

Programs

Maple

b:= proc(n, k) option remember; `if`(n=0, 1, add(
      b(n-i, k)*binomial(n, i), i=1..min(n, k)))
    end:
a:= n-> (k-> b(n, k) -b(n, k-1))(8):
seq(a(n), n=8..25);

Formula

E.g.f.: 1/(1-Sum_{i=1..8} x^i/i!) - 1/(1-Sum_{i=1..7} x^i/i!).

a(n) = A276928(n) - A276927(n).