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A320761 Number of ordered set partitions of [n] where the maximal block size equals five.

%I A320761 #7 Dec 14 2020 05:13:40
%S A320761 1,12,168,2464,38808,657972,11997216,234594360,4903616718,
%T A320761 109205019924,2582909885556,64686057980544,1710536977653504,
%U A320761 47637803779229664,1393903719674129664,42758329987344875904,1372254504736418142840,45989719374155059863360
%N A320761 Number of ordered set partitions of [n] where the maximal block size equals five.
%H A320761 Alois P. Heinz, <a href="/A320761/b320761.txt">Table of n, a(n) for n = 5..424</a>
%F A320761 E.g.f.: 1/(1-Sum_{i=1..5} x^i/i!) - 1/(1-Sum_{i=1..4} x^i/i!).
%F A320761 a(n) = A276925(n) - A276924(n).
%p A320761 b:= proc(n, k) option remember; `if`(n=0, 1, add(
%p A320761       b(n-i, k)*binomial(n, i), i=1..min(n, k)))
%p A320761     end:
%p A320761 a:= n-> (k-> b(n, k) -b(n, k-1))(5):
%p A320761 seq(a(n), n=5..25);
%t A320761 b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[b[n - i, k] Binomial[n, i], {i, 1, Min[n, k]}]];
%t A320761 a[n_] := With[{k = 5}, b[n, k] - b[n, k-1]];
%t A320761 a /@ Range[5, 25] (* _Jean-François Alcover_, Dec 14 2020, after _Alois P. Heinz_ *)
%Y A320761 Column k=5 of A276922.
%Y A320761 Cf. A276924, A276925.
%K A320761 nonn
%O A320761 5,2
%A A320761 _Alois P. Heinz_, Oct 20 2018