OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..449
Kévin Perrot, Sylvain Sené, and Léah Tapin, On countings and enumerations of block-parallel automata networks, arXiv:2304.09664 [cs.DM], 2023.
FORMULA
a(n) = Sum_{d|n} n!/(n/d)!^d.
E.g.f.: Sum_{k>0} x^k/(k!-x^k). - Vladeta Jovovic, Oct 13 2003
a(n) ~ n!. - Vaclav Kotesovec, Jul 21 2019
EXAMPLE
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.
MAPLE
A061095 := n -> add(n!/(n/d)!^d, d = numtheory[divisors](n));
seq(A061095 (n), n = 1..17); # Peter Luschny, Apr 13 2011
MATHEMATICA
Table[Sum[n!/(n/d)!^d, {d, Divisors[n]}], {n, 1, 20}] (* Geoffrey Critzer, Aug 18 2011 *)
PROG
(PARI) /* compare to A038041 */
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); }
vector(33, n, A061095(n)) /* Joerg Arndt, Apr 16 2011 */
(PARI) a(n)=sumdiv(n, d, n!/(n/d)!^d ); \\ Joerg Arndt, Feb 23 2014
CROSSREFS
KEYWORD
nonn,nice,easy
AUTHOR
Henry Bottomley, May 29 2001
STATUS
approved