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A332949 Number of entries in the ninth blocks of all set partitions of [n] when blocks are ordered by increasing lengths.

%I A332949 #6 Mar 04 2020 09:41:02
%S A332949 1,91,2531,56717,1052130,17011450,248006774,3363718597,43354519587,
%T A332949 537399621668,6456347423794,75743936924077,874027443321519,
%U A332949 9978667891988711,113225455087566673,1281748270131892718,14527578406583077101,165413377044356558731
%N A332949 Number of entries in the ninth blocks of all set partitions of [n] when blocks are ordered by increasing lengths.
%H A332949 Alois P. Heinz, <a href="/A332949/b332949.txt">Table of n, a(n) for n = 9..576</a>
%H A332949 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%p A332949 b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i>n, 0,
%p A332949       add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))(b(n-i*j, i+1,
%p A332949       max(0, t-j))/j!*combinat[multinomial](n, i$j, n-i*j)), j=0..n/i)))
%p A332949     end:
%p A332949 a:= n-> b(n, 1, 9)[2]:
%p A332949 seq(a(n), n=9..26);
%Y A332949 Column k=9 of A319298.
%K A332949 nonn
%O A332949 9,2
%A A332949 _Alois P. Heinz_, Mar 03 2020