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A038041 Number of ways to partition an n-set into subsets of equal size. 58
1, 2, 2, 5, 2, 27, 2, 142, 282, 1073, 2, 32034, 2, 136853, 1527528, 4661087, 2, 227932993, 2, 3689854456, 36278688162, 13749663293, 2, 14084955889019, 5194672859378, 7905858780927, 2977584150505252, 13422745388226152, 2, 1349877580746537123, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..250

FORMULA

a(n) = Sum_{d divides n} (n!/(d!*((n/d)!)^d)).

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

EXAMPLE

a(4) = card{ 1|2|3|4, 12|34, 14|23, 13|24, 1234 } = 5.

MAPLE

A038041 := proc(n) local d;

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

seq(A038041(n), n = 1..29); # Peter Luschny, Apr 16 2011

MATHEMATICA

a[n_] := Block[{d = Divisors@ n}, Plus @@ (n!/(#! (n/#)!^#) & /@ d)]; Array[a, 29] (* Robert G. Wilson v, Apr 16 2011 *)

Table[Sum[n!/((n/d)!*(d!)^(n/d)), {d, Divisors[n]}], {n, 1, 31}] (* Emanuele Munarini, Jan 30 2014 *)

PROG

(PARI)  /* compare to A061095 */

mnom(v)=

/* Multinomial coefficient s! / prod(j=1, n, v[j]!) where

  s= sum(j=1, n, v[j]) and n is the number of elements in v[]. */

sum(j=1, #v, v[j])! / prod(j=1, #v, v[j]!)

A038041(n)={local(r=0); fordiv(n, d, r+=mnom(vector(d, j, n/d))/d!); return(r); }

vector(33, n, A038041(n)) /* Joerg Arndt, Apr 16 2011 */

(Maxima) a(n):= lsum(n!/((n/d)!*(d!)^(n/d)), d, listify(divisors(n)));

makelist(a(n), n, 1, 40); /* Emanuele Munarini, Feb 03 2014 */

CROSSREFS

Cf. A061095 (same but with labeled boxes), A005225, A236696, A055225, A262280, A262320.

Column k=1 of A208437.

Sequence in context: A324505 A226135 A284464 * A197591 A097891 A097611

Adjacent sequences:  A038038 A038039 A038040 * A038042 A038043 A038044

KEYWORD

nonn,easy

AUTHOR

Christian G. Bower

EXTENSIONS

More terms from Erich Friedman.

STATUS

approved

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Last modified March 25 08:15 EDT 2019. Contains 321469 sequences. (Running on oeis4.)