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A232664
Number of permutations of order n-1 such that no proper partial sum is zero modulo n.
1
1, 1, 2, 4, 16, 56, 408, 2376, 19920, 156096, 1711680, 16851072, 216434304, 2557907712, 38102969088
OFFSET
1,3
LINKS
FORMULA
For n>1, a(n) = A232663(n) / (n-1-(n mod 2)).
EXAMPLE
For n=5, the permutation (1,2,4,3) has proper partial sums 1, 1+2=3, 1+2+4=7, neither of which is zero modulo n. The number of such permutations is a(5)=16.
PROG
(PARI) { a(n) = my(r=0, q, s, g); for(i=1, (n-1)!, q=numtoperm(n-1, i); s=Mod(0, n); g=1; for(j=1, n-2, s+=q[j]; if(s==0, g=0; break)); r+=g); r }
CROSSREFS
Sequence in context: A235459 A081919 A362524 * A153954 A275764 A053349
KEYWORD
nonn,more
AUTHOR
Max Alekseyev, Nov 27 2013
STATUS
approved