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A038041
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Number of ways to partition a set into subsets of equal size.
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10
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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; internal format)
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OFFSET
| 1,2
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 1..250
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FORMULA
| a(n) = Sum_{d divides n} (n!/(d!*((n/d)!)^d)).
E.g.f.: Sum_{k >= 1} (exp(x^k/k!)-1).
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EXAMPLE
| a(4) = card{ 1|2|3|4, 12|34, 14|23, 13|24, 1234 } = 5.
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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
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MATHEMATICA
| f[n_] := Block[{d = Divisors@ n}, Plus @@ (n!/(#! (n/#)!^#) & /@ d)]; Array[f, 29] (* Robert G. Wilson v, Apr 16 2011 *)
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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[]. */
{ return( 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)) /* show terms */ /* Joerg Arndt, Apr 16 2011 */
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CROSSREFS
| Cf. A061095 (same but with labeled boxes).
Sequence in context: A144943 A114976 A085483 * A197591 A097891 A097611
Adjacent sequences: A038038 A038039 A038040 * A038042 A038043 A038044
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KEYWORD
| nonn,easy
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AUTHOR
| Christian G. Bower (bowerc(AT)usa.net)
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EXTENSIONS
| More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
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