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A373422
Triangle read by rows: T(n,k) = number of permutations of [n] starting from k that have zero (n-1)-th differences. (n>=1, 1<=k<=n).
1
0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 4, 2, 4, 2, 4, 3, 0, 0, 0, 0, 3, 40, 36, 40, 40, 40, 36, 40, 29, 0, 0, 0, 0, 0, 0, 29, 232, 152, 240, 200, 208, 200, 240, 152, 232, 235, 142, 140, 257, 168, 168, 257, 140, 142, 235, 11712, 13216, 12208, 12384, 11408, 11136, 11408, 12384, 12208, 13216, 11712
OFFSET
1,11
LINKS
Seiichi Manyama, Rows n = 1..14, flattened
FORMULA
T(n,k) = T(n,n+1-k) for 1<=k<=n.
If p is prime, T(p+1,k) = 0 for 2 <= k <= p.
EXAMPLE
T(3,1) = 1 because [1,2,3] have zero 2nd differences.
1 2 3
1 1
0
Triangle starts:
0;
0, 0;
1, 0, 1;
1, 0, 0, 1;
4, 2, 4, 2, 4;
3, 0, 0, 0, 0, 3;
40, 36, 40, 40, 40, 36, 40;
29, 0, 0, 0, 0, 0, 0, 29;
232, 152, 240, 200, 208, 200, 240, 152, 232;
235, 142, 140, 257, 168, 168, 257, 140, 142, 235;
PROG
(PARI) tabl(n) = my(nn=vector(n)); forperm([1..n], p, if(sum(k=1, n, (-1)^k*binomial(n-1, k-1)*p[k])==0, nn[p[1]]++)); nn;
CROSSREFS
Row sums give 2 * A131502(n-1).
Sequence in context: A178253 A209272 A105397 * A328999 A236185 A300004
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Jun 04 2024
STATUS
approved