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A262320 Number of ways to select a subset s from an n-set and then partition s into blocks of equal size.

%I A262320 #12 Dec 18 2016 10:33:54
%S A262320 1,2,5,12,30,73,191,528,1553,5032,18088,66905,266382,1164517,5215645,
%T A262320 23868104,117740144,609872351,3268548407,18110463456,102867877415,
%U A262320 620476915966,4005216028162,25747549921339,166978155172421,1168774024335204,8556355097320142
%N A262320 Number of ways to select a subset s from an n-set and then partition s into blocks of equal size.
%H A262320 Alois P. Heinz, <a href="/A262320/b262320.txt">Table of n, a(n) for n = 0..616</a>
%F A262320 E.g.f.: exp(x) * (1 + Sum_{k>=1} (exp(x^k/k!)-1)).
%F A262320 a(n) = 1 + Sum_{k=1..n} C(n,k) * A038041(k).
%F A262320 a(n) = 1 + A262280(n).
%F A262320 a(n) = Sum_{k=0..n} A262321(k).
%e A262320 a(3) = 12: {}, 1, 2, 3, 12, 1|2, 13, 1|3, 23, 2|3, 123, 1|2|3.
%p A262320 b:= proc(n) option remember;
%p A262320       add(1/(d!*(n/d)!^d), d=numtheory[divisors](n))
%p A262320     end:
%p A262320 a:= n-> 1 + n! * add(b(k)/(n-k)!, k=1..n):
%p A262320 seq(a(n), n=0..30);
%t A262320 b[n_] := b[n] = DivisorSum[n, 1/(#!*(n/#)!^#)&]; a[n_] := 1 + n! * Sum[b[k]/(n-k)!, {k, 1, n}]; Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Dec 18 2016, after _Alois P. Heinz_ *)
%Y A262320 Partial sums of A262321.
%Y A262320 Cf. A038041, A262280.
%K A262320 nonn
%O A262320 0,2
%A A262320 _Alois P. Heinz_, Sep 17 2015