# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a320759 Showing 1-1 of 1 %I A320759 #7 Dec 14 2020 05:13:21 %S A320759 1,8,80,860,10290,136080,1977360,31365600,539847000,10026139200, %T A320759 199937337600,4262167509600,96744738090000,2329950823200000, %U A320759 59348032327584000,1594257675506496000,45047749044458160000,1335740755933584000000,41473196779273459200000 %N A320759 Number of ordered set partitions of [n] where the maximal block size equals three. %H A320759 Alois P. Heinz, Table of n, a(n) for n = 3..424 %F A320759 E.g.f.: 1/(1-Sum_{i=1..3} x^i/i!) - 1/(1-Sum_{i=1..2} x^i/i!). %F A320759 a(n) = A189886(n) - A080599(n). %p A320759 b:= proc(n, k) option remember; `if`(n=0, 1, add( %p A320759 b(n-i, k)*binomial(n, i), i=1..min(n, k))) %p A320759 end: %p A320759 a:= n-> (k-> b(n, k) -b(n, k-1))(3): %p A320759 seq(a(n), n=3..25); %t A320759 b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[b[n - i, k] Binomial[n, i], {i, 1, Min[n, k]}]]; %t A320759 a[n_] := With[{k = 3}, b[n, k] - b[n, k-1]]; %t A320759 a /@ Range[3, 25] (* _Jean-François Alcover_, Dec 14 2020, after _Alois P. Heinz_ *) %Y A320759 Column k=3 of A276922. %Y A320759 Cf. A080599, A189886. %K A320759 nonn %O A320759 3,2 %A A320759 _Alois P. Heinz_, Oct 20 2018 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE