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A061095
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Number of ways of dividing n labeled items into labeled boxes with an equal number of items in each box.
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18
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1, 3, 7, 31, 121, 831, 5041, 42911, 364561, 3742453, 39916801, 486891175, 6227020801, 87859375033, 1307843292757, 21004582611871, 355687428096001, 6415015584161757, 121645100408832001, 2435278206317164781, 51091124681475552961, 1124549556257968545433
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = Sum_{d|n} n!/(n/d)!^d.
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EXAMPLE
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a(6) = 720+90+20+1 = 831 since 720 ways of evenly distributing six labeled items into six labeled boxes, 90 into three, 20 into two and 1 into one.
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MAPLE
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A061095 := n -> add(n!/(n/d)!^d, d = numtheory[divisors](n));
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MATHEMATICA
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Table[Sum[n!/(n/d)!^d, {d, Divisors[n]}], {n, 1, 20}] (* Geoffrey Critzer, Aug 18 2011 *)
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PROG
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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]!)
A061095(n)={local(r=0); fordiv(n, d, r+=mnom(vector(d, j, n/d))); return(r); }
(PARI) a(n)=sumdiv(n, d, n!/(n/d)!^d ); \\ Joerg Arndt, Feb 23 2014
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CROSSREFS
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KEYWORD
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nonn,nice,easy
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AUTHOR
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STATUS
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approved
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