A232664 - OEIS

%I #11 Nov 30 2013 21:49:04

%S 1,1,2,4,16,56,408,2376,19920,156096,1711680,16851072,216434304,

%T 2557907712,38102969088

%N Number of permutations of order n-1 such that no proper partial sum is zero modulo n.

%H K. Gaitanas, <a href="http://mathoverflow.net/questions/149998/avoiding-multiples-of-p">Avoiding multiples of p</a>, MathOverflow.

%F For n>1, a(n) = A232663(n) / (n-1-(n mod 2)).

%e 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.

%o (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 }

%K nonn,more

%O 1,3

%A _Max Alekseyev_, Nov 27 2013