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

7,2

Links

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

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).

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);

Crossrefs

Column k=7 of A276922.

Cf. A276926, A276927.

Sequence in context: A218517 A230347 A182608 * A225194 A027776 A140770

Adjacent sequences: A320760 A320761 A320762 * A320764 A320765 A320766

Keyword

nonn

Author

Alois P. Heinz, Oct 20 2018

Status

approved