A349277 Triangle T(n,k), n >= 1, 1 <= k <= n, read by rows, where T(n,k) is the number of permutations p of [n] such that Sum_{j=1..n} j/p(j) is an integer and p(n) = k.

1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 2, 1, 1, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 8, 4, 4, 2, 2, 0, 2, 0, 8, 18, 18, 14, 18, 0, 14, 0, 0, 22, 113, 130, 102, 135, 108, 122, 0, 314, 0, 104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1128, 1152, 1166, 1130, 1078, 1334, 1182, 0, 1734, 3390, 1226, 0, 1128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14520

Offset: 1

Author

Seiichi Manyama, Nov 12 2021

Keywords

• nonn
• tabl

Examples

			Triangle begins:
    1;
    0,   1;
    0,   0,   1;
    1,   0,   0,   1;
    0,   0,   0,   0,   2;
    1,   1,   2,   2,   0,   2;
    0,   0,   0,   0,   0,   0, 8;
    4,   4,   2,   2,   0,   2, 0,   8;
   18,  18,  14,  18,   0,  14, 0,   0, 22;
  113, 130, 102, 135, 108, 122, 0, 314,  0, 104;
    0,   0,   0,   0,   0,   0, 0,   0,  0,   0, 1128;
		

Crossrefs

Row sum gives A073090.

Programs

Ruby

def A(n)
  ary = Array.new(n, 0)
  (1..n).to_a.permutation{|i|
    ary[i[-1] - 1] += 1 if (1..n).inject(0){|s, j| s + j / i[j - 1].to_r}.denominator == 1
  }
  ary
end
def A349277(n)
  (1..n).map{|i| A(i)}.flatten
end
p A349277(8)

Formula

If n is prime, T(n,k) = 0 for 1 <= k <= n-1.

T(n,n) = A073090(n-1).