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A320760 Number of ordered set partitions of [n] where the maximal block size equals four.

%I A320760 #7 Dec 14 2020 05:13:29
%S A320760 1,10,120,1540,21490,326970,5402250,96500250,1855334250,38228190000,
%T A320760 840776937000,19666511865000,487617137007000,12776791730703000,
%U A320760 352825452012033000,10242418813814187000,311854958169459705000,9937942309809373860000,330821844137019184950000
%N A320760 Number of ordered set partitions of [n] where the maximal block size equals four.
%H A320760 Alois P. Heinz, <a href="/A320760/b320760.txt">Table of n, a(n) for n = 4..424</a>
%F A320760 E.g.f.: 1/(1-Sum_{i=1..4} x^i/i!) - 1/(1-Sum_{i=1..3} x^i/i!).
%F A320760 a(n) = A276924(n) - A189886(n).
%p A320760 b:= proc(n, k) option remember; `if`(n=0, 1, add(
%p A320760       b(n-i, k)*binomial(n, i), i=1..min(n, k)))
%p A320760     end:
%p A320760 a:= n-> (k-> b(n, k) -b(n, k-1))(4):
%p A320760 seq(a(n), n=4..25);
%t A320760 b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[b[n - i, k] Binomial[n, i], {i, 1, Min[n, k]}]];
%t A320760 a[n_] := With[{k = 4}, b[n, k] - b[n, k-1]];
%t A320760 a /@ Range[4, 25] (* _Jean-François Alcover_, Dec 14 2020, after _Alois P. Heinz_ *)
%Y A320760 Column k=4 of A276922.
%Y A320760 Cf. A189886, A276924.
%K A320760 nonn
%O A320760 4,2
%A A320760 _Alois P. Heinz_, Oct 20 2018