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A131502
Half the number of permutations of 0..n with a zero n-th difference.
4
0, 0, 1, 1, 8, 3, 136, 29, 928, 942, 66496, 6175, 2785856, 205678, 11122048
OFFSET
0,5
EXAMPLE
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.
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 *)
PROG
(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]<p[-1] and not sum(c[i]*p[i] for i in range(n+1))) # Chai Wah Wu, Jun 04 2024
CROSSREFS
Sequence in context: A038281 A302370 A303086 * A302891 A303626 A100253
KEYWORD
nonn,more
AUTHOR
R. H. Hardin, Aug 13 2007
STATUS
approved