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A332950 Number of entries in the tenth blocks of all set partitions of [n] when blocks are ordered by increasing lengths.

%I A332950 #6 Mar 04 2020 09:52:39
%S A332950 1,111,3697,97605,2126580,40204179,681004277,10645001317,156970929310,
%T A332950 2213900198635,30121302914917,398061723460524,5142929025812977,
%U A332950 65335359570066118,819943536213362166,10204014403455526051,126342880437736660311,1561117416681285339037
%N A332950 Number of entries in the tenth blocks of all set partitions of [n] when blocks are ordered by increasing lengths.
%H A332950 Alois P. Heinz, <a href="/A332950/b332950.txt">Table of n, a(n) for n = 10..576</a>
%H A332950 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%p A332950 b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i>n, 0,
%p A332950       add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))(b(n-i*j, i+1,
%p A332950       max(0, t-j))/j!*combinat[multinomial](n, i$j, n-i*j)), j=0..n/i)))
%p A332950     end:
%p A332950 a:= n-> b(n, 1, 10)[2]:
%p A332950 seq(a(n), n=10..27);
%Y A332950 Column k=10 of A319298.
%K A332950 nonn
%O A332950 10,2
%A A332950 _Alois P. Heinz_, Mar 03 2020