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A320766 Number of ordered set partitions of [n] where the maximal block size equals ten.

%I A320766 #4 Oct 20 2018 18:08:27
%S A320766 1,22,528,12584,308308,7843836,208111904,5767576672,167004507384,
%T A320766 5050066185736,159340977018652,5240336900883084,179428070995076904,
%U A320766 6388579669849124748,236257342145458744968,9064169856705631376280,360365153529146965326270
%N A320766 Number of ordered set partitions of [n] where the maximal block size equals ten.
%H A320766 Alois P. Heinz, <a href="/A320766/b320766.txt">Table of n, a(n) for n = 10..426</a>
%F A320766 E.g.f.: 1/(1-Sum_{i=1..10} x^i/i!) - 1/(1-Sum_{i=1..9} x^i/i!).
%F A320766 a(n) = A276930(n) - A276929(n).
%p A320766 b:= proc(n, k) option remember; `if`(n=0, 1, add(
%p A320766       b(n-i, k)*binomial(n, i), i=1..min(n, k)))
%p A320766     end:
%p A320766 a:= n-> (k-> b(n, k) -b(n, k-1))(10):
%p A320766 seq(a(n), n=10..30);
%Y A320766 Column k=10 of A276922.
%Y A320766 Cf. A276929, A276930.
%K A320766 nonn
%O A320766 10,2
%A A320766 _Alois P. Heinz_, Oct 20 2018