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

%I A320763 #4 Oct 20 2018 17:57:31
%S A320763 1,16,288,5280,101640,2068704,44595408,1017804216,24559319070,
%T A320763 625388375040,16772475939648,472802783660064,13981054231585584,
%U A320763 432866241024085440,14006847775868101440,472893544571144089536,16631451859811919417144,608402197372214335559040
%N A320763 Number of ordered set partitions of [n] where the maximal block size equals seven.
%H A320763 Alois P. Heinz, <a href="/A320763/b320763.txt">Table of n, a(n) for n = 7..425</a>
%F A320763 E.g.f.: 1/(1-Sum_{i=1..7} x^i/i!) - 1/(1-Sum_{i=1..6} x^i/i!).
%F A320763 a(n) = A276927(n) - A276926(n).
%p A320763 b:= proc(n, k) option remember; `if`(n=0, 1, add(
%p A320763       b(n-i, k)*binomial(n, i), i=1..min(n, k)))
%p A320763     end:
%p A320763 a:= n-> (k-> b(n, k) -b(n, k-1))(7):
%p A320763 seq(a(n), n=7..25);
%Y A320763 Column k=7 of A276922.
%Y A320763 Cf. A276926, A276927.
%K A320763 nonn
%O A320763 7,2
%A A320763 _Alois P. Heinz_, Oct 20 2018