%I #6 Mar 04 2020 09:41:02

%S 1,91,2531,56717,1052130,17011450,248006774,3363718597,43354519587,

%T 537399621668,6456347423794,75743936924077,874027443321519,

%U 9978667891988711,113225455087566673,1281748270131892718,14527578406583077101,165413377044356558731

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

%H Alois P. Heinz, <a href="/A332949/b332949.txt">Table of n, a(n) for n = 9..576</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>

%p b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i>n, 0,

%p add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))(b(n-i*j, i+1,

%p max(0, t-j))/j!*combinat[multinomial](n, i$j, n-i*j)), j=0..n/i)))

%p end:

%p a:= n-> b(n, 1, 9)[2]:

%p seq(a(n), n=9..26);

%Y Column k=9 of A319298.

%K nonn

%O 9,2

%A _Alois P. Heinz_, Mar 03 2020