A320762 Number of ordered set partitions of [n] where the maximal block size equals six.

1, 14, 224, 3696, 64680, 1206744, 24011988, 508864356, 11459682234, 273563089800, 6904861371408, 183819838041840, 5149305370473264, 151447801937560128, 4666989813249123360, 150394712706368466336, 5059062167993588722968, 177346570951333803395376

Offset: 6

Author

Alois P. Heinz, Oct 20 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 6..424

Crossrefs

Column k=6 of A276922.

Cf. A276925, A276926.

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))(6):
seq(a(n), n=6..25);

Formula

E.g.f.: 1/(1-Sum_{i=1..6} x^i/i!) - 1/(1-Sum_{i=1..5} x^i/i!).

a(n) = A276926(n) - A276925(n).