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

9,2

Links

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

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).

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);

Crossrefs

Column k=9 of A276922.

Cf. A276928, A276929.

Sequence in context: A109116 A190922 A136257 * A099278 A276452 A111158

Adjacent sequences: A320762 A320763 A320764 * A320766 A320767 A320768

Keyword

nonn

Author

Alois P. Heinz, Oct 20 2018

Status

approved