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A262280 Number of ways to select a nonempty subset s from an n-set and then partition s into blocks of equal size.

%I A262280 #16 Feb 15 2017 11:27:20
%S A262280 0,1,4,11,29,72,190,527,1552,5031,18087,66904,266381,1164516,5215644,
%T A262280 23868103,117740143,609872350,3268548406,18110463455,102867877414,
%U A262280 620476915965,4005216028161,25747549921338,166978155172420,1168774024335203,8556355097320141
%N A262280 Number of ways to select a nonempty subset s from an n-set and then partition s into blocks of equal size.
%H A262280 Alois P. Heinz, <a href="/A262280/b262280.txt">Table of n, a(n) for n = 0..616</a>
%F A262280 E.g.f.: exp(x) * Sum_{k>=1} (exp(x^k/k!)-1).
%F A262280 a(n) = Sum_{k=1..n} C(n,k) * A038041(k).
%F A262280 a(n) = A262320(n) - 1.
%e A262280 a(3) = 11: 1, 2, 3, 12, 1|2, 13, 1|3, 23, 2|3, 123, 1|2|3.
%p A262280 b:= proc(n) option remember;
%p A262280       add(1/(d!*(n/d)!^d), d=numtheory[divisors](n))
%p A262280     end:
%p A262280 a:= n-> n! * add(b(k)/(n-k)!, k=1..n):
%p A262280 seq(a(n), n=0..30);
%t A262280 b[n_] := b[n] = DivisorSum[n, 1/(#!*(n/#)!^#)&]; a[n_] := n!*Sum[b[k]/(n-k)!, {k, 1, n}]; Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Feb 15 2017, translated from Maple *)
%Y A262280 Cf. A038041, A262320.
%K A262280 nonn
%O A262280 0,3
%A A262280 _Alois P. Heinz_, Sep 17 2015