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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. 3
0, 1, 4, 11, 29, 72, 190, 527, 1552, 5031, 18087, 66904, 266381, 1164516, 5215644, 23868103, 117740143, 609872350, 3268548406, 18110463455, 102867877414, 620476915965, 4005216028161, 25747549921338, 166978155172420, 1168774024335203, 8556355097320141 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..616

FORMULA

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

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

a(n) = A262320(n) - 1.

EXAMPLE

a(3) = 11: 1, 2, 3, 12, 1|2, 13, 1|3, 23, 2|3, 123, 1|2|3.

MAPLE

b:= proc(n) option remember;

      add(1/(d!*(n/d)!^d), d=numtheory[divisors](n))

    end:

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

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

MATHEMATICA

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-Fran├žois Alcover, Feb 15 2017, translated from Maple *)

CROSSREFS

Cf. A038041, A262320.

Sequence in context: A220018 A131046 A109803 * A027968 A027970 A027972

Adjacent sequences:  A262277 A262278 A262279 * A262281 A262282 A262283

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 17 2015

STATUS

approved

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Last modified September 24 04:42 EDT 2020. Contains 337317 sequences. (Running on oeis4.)