A320763 Number of ordered set partitions of [n] where the maximal block size equals seven.

1, 16, 288, 5280, 101640, 2068704, 44595408, 1017804216, 24559319070, 625388375040, 16772475939648, 472802783660064, 13981054231585584, 432866241024085440, 14006847775868101440, 472893544571144089536, 16631451859811919417144, 608402197372214335559040

Offset: 7

Author

Alois P. Heinz, Oct 20 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..425

Crossrefs

Column k=7 of A276922.

Cf. A276926, A276927.

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))(7):
seq(a(n), n=7..25);

Formula

E.g.f.: 1/(1-Sum_{i=1..7} x^i/i!) - 1/(1-Sum_{i=1..6} x^i/i!).

a(n) = A276927(n) - A276926(n).