A131502 Half the number of permutations of 0..n with a zero n-th difference.

0, 0, 1, 1, 8, 3, 136, 29, 928, 942, 66496, 6175, 2785856, 205678, 11122048

Offset: 0

Author

R. H. Hardin, Aug 13 2007

Keywords

• nonn
• more

Examples

			a(5)=3 because 0,1,2,3,4,5 ; 0,2,4,3,1,5 ; and 0,4,2,1,3,5 ; and their reverses have zero 5th differences.
		

Programs

Mathematica

(* naive and memory intensive implementation generating all permutations *)
Table[Count[
  Map[Differences[#, n - 1] &,
   Take[Permutations[Range[1, n]], Max[1, n!/2]]], {0}], {n, 1, 10}] (* Olivier Gérard, May 30 2024 *)

Python

from math import comb
from itertools import permutations
def A131502(n):
    c = [-comb(n,i) if i&1 else comb(n,i) for i in range(n+1)]
    return sum(1 for p in permutations(range(n+1)) if p[0]Chai Wah Wu, Jun 04 2024