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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. 4

%I

%S 1,2,5,12,30,73,191,528,1553,5032,18088,66905,266382,1164517,5215645,

%T 23868104,117740144,609872351,3268548407,18110463456,102867877415,

%U 620476915966,4005216028162,25747549921339,166978155172421,1168774024335204,8556355097320142

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

%H Alois P. Heinz, <a href="/A262320/b262320.txt">Table of n, a(n) for n = 0..616</a>

%F E.g.f.: exp(x) * (1 + Sum_{k>=1} (exp(x^k/k!)-1)).

%F a(n) = 1 + Sum_{k=1..n} C(n,k) * A038041(k).

%F a(n) = 1 + A262280(n).

%F a(n) = Sum_{k=0..n} A262321(k).

%e a(3) = 12: {}, 1, 2, 3, 12, 1|2, 13, 1|3, 23, 2|3, 123, 1|2|3.

%p b:= proc(n) option remember;

%p end:

%p a:= n-> 1 + n! * add(b(k)/(n-k)!, k=1..n):

%p seq(a(n), n=0..30);

%t 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 Partial sums of A262321.

%Y Cf. A038041, A262280.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Sep 17 2015

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Last modified August 11 08:50 EDT 2020. Contains 336422 sequences. (Running on oeis4.)