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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 (list; graph; refs; listen; history; text; internal format)
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: A009290 A235459 A081919 * A153954 A275764 A053349

Adjacent sequences:  A232661 A232662 A232663 * A232665 A232666 A232667

KEYWORD

nonn,more

AUTHOR

Max Alekseyev, Nov 27 2013

STATUS

approved

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Last modified September 30 14:56 EDT 2020. Contains 337439 sequences. (Running on oeis4.)