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

%I A320765 #4 Oct 20 2018 18:05:14
%S A320765 1,20,440,9680,220220,5229224,130069940,3392692160,92780281880,
%T A320765 2657929522820,79670485645608,2495398380120360,81558207395885220,
%U A320765 2777643033619233780,98440545801322467600,3625667341827832048176,138601954935720474004950,5492809832014657114548300
%N A320765 Number of ordered set partitions of [n] where the maximal block size equals nine.
%H A320765 Alois P. Heinz, <a href="/A320765/b320765.txt">Table of n, a(n) for n = 9..426</a>
%F A320765 E.g.f.: 1/(1-Sum_{i=1..9} x^i/i!) - 1/(1-Sum_{i=1..8} x^i/i!).
%F A320765 a(n) = A276929(n) - A276928(n).
%p A320765 b:= proc(n, k) option remember; `if`(n=0, 1, add(
%p A320765       b(n-i, k)*binomial(n, i), i=1..min(n, k)))
%p A320765     end:
%p A320765 a:= n-> (k-> b(n, k) -b(n, k-1))(9):
%p A320765 seq(a(n), n=9..25);
%Y A320765 Column k=9 of A276922.
%Y A320765 Cf. A276928, A276929.
%K A320765 nonn
%O A320765 9,2
%A A320765 _Alois P. Heinz_, Oct 20 2018