A232664 Number of permutations of order n-1 such that no proper partial sum is zero modulo n.

1, 1, 2, 4, 16, 56, 408, 2376, 19920, 156096, 1711680, 16851072, 216434304, 2557907712, 38102969088

Offset

1,3

Links

Table of n, a(n) for n=1..15.

K. Gaitanas, Avoiding multiples of p, MathOverflow.

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

Adjacent sequences: A232661 A232662 A232663 * A232665 A232666 A232667

Keyword

nonn,more

Author

Max Alekseyev, Nov 27 2013

Status

approved