A332946 - OEIS

%I #5 Mar 03 2020 17:02:06

%S 1,43,617,7681,79756,741665,6467891,54658254,451897330,3685879069,

%T 30091146181,248749105815,2091117462980,17933165800591,

%U 157654535847037,1426401197217090,13303368764700743,127934361462621048,1268098183967052868,12948542410221048226

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

%H Alois P. Heinz, <a href="/A332946/b332946.txt">Table of n, a(n) for n = 6..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, 6)[2]:

%p seq(a(n), n=6..25);

%Y Column k=6 of A319298.

%K nonn

%O 6,2

%A _Alois P. Heinz_, Mar 03 2020