A320765 Number of ordered set partitions of [n] where the maximal block size equals nine.

1, 20, 440, 9680, 220220, 5229224, 130069940, 3392692160, 92780281880, 2657929522820, 79670485645608, 2495398380120360, 81558207395885220, 2777643033619233780, 98440545801322467600, 3625667341827832048176, 138601954935720474004950, 5492809832014657114548300

Offset: 9

Author

Alois P. Heinz, Oct 20 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 9..426

Crossrefs

Column k=9 of A276922.

Cf. A276928, A276929.

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))(9):
seq(a(n), n=9..25);

Formula

E.g.f.: 1/(1-Sum_{i=1..9} x^i/i!) - 1/(1-Sum_{i=1..8} x^i/i!).

a(n) = A276929(n) - A276928(n).