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A262321 Number of ways to select a subset s containing n from {1,...,n} and then partition s into blocks of equal size. 2
1, 1, 3, 7, 18, 43, 118, 337, 1025, 3479, 13056, 48817, 199477, 898135, 4051128, 18652459, 93872040, 492132207, 2658676056, 14841915049, 84757413959, 517609038551, 3384739112196, 21742333893177, 141230605251082, 1001795869162783, 7387581072984938 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(0) = 1 by convention.

LINKS

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

FORMULA

E.g.f.: A(x) - Integral_{x} A(x) dx, with A(x) = e.g.f. of A262320.

EXAMPLE

a(0) = 1: {}.

a(1) = 1: 1.

a(2) = 3: 2, 12, 1|2.

a(3) = 7: 3, 13, 1|3, 23, 2|3, 123, 1|2|3.

a(4) = 18: 4, 14, 1|4, 24, 2|4, 34, 3|4, 124, 1|2|4, 134, 1|3|4, 234, 2|3|4, 1234, 12|34, 13|24, 14|23, 1|2|3|4.

MAPLE

b:= proc(n) option remember; n!*`if`(n=0, 1,

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

    end:

a:= n-> add(b(k)*binomial(n-1, k-1), k=0..n):

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

MATHEMATICA

b[n_] := b[n] = n!*If[n == 0, 1, DivisorSum[n, 1/(#!*(n/#)!^#)&]];

a[n_] :=  Sum[b[k]*Binomial[n-1, k-1], {k, 0, n}];

Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, Mar 28 2017, translated from Maple *)

CROSSREFS

First differences of A262320.

Sequence in context: A091621 A129921 A036670 * A182995 A027967 A181306

Adjacent sequences:  A262318 A262319 A262320 * A262322 A262323 A262324

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 18 2015

STATUS

approved

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Last modified July 12 06:21 EDT 2020. Contains 335658 sequences. (Running on oeis4.)