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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.

%I A349277 #26 Nov 13 2021 06:00:06
%S A349277 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,
%T A349277 0,8,18,18,14,18,0,14,0,0,22,113,130,102,135,108,122,0,314,0,104,0,0,
%U A349277 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
%N 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.
%F A349277 If n is prime, T(n,k) = 0 for 1 <= k <= n-1.
%F A349277 T(n,n) = A073090(n-1).
%e A349277 Triangle begins:
%e A349277     1;
%e A349277     0,   1;
%e A349277     0,   0,   1;
%e A349277     1,   0,   0,   1;
%e A349277     0,   0,   0,   0,   2;
%e A349277     1,   1,   2,   2,   0,   2;
%e A349277     0,   0,   0,   0,   0,   0, 8;
%e A349277     4,   4,   2,   2,   0,   2, 0,   8;
%e A349277    18,  18,  14,  18,   0,  14, 0,   0, 22;
%e A349277   113, 130, 102, 135, 108, 122, 0, 314,  0, 104;
%e A349277     0,   0,   0,   0,   0,   0, 0,   0,  0,   0, 1128;
%o A349277 (Ruby)
%o A349277 def A(n)
%o A349277   ary = Array.new(n, 0)
%o A349277   (1..n).to_a.permutation{|i|
%o A349277     ary[i[-1] - 1] += 1 if (1..n).inject(0){|s, j| s + j / i[j - 1].to_r}.denominator == 1
%o A349277   }
%o A349277   ary
%o A349277 end
%o A349277 def A349277(n)
%o A349277   (1..n).map{|i| A(i)}.flatten
%o A349277 end
%o A349277 p A349277(8)
%Y A349277 Row sum gives A073090.
%K A349277 nonn,tabl
%O A349277 1,15
%A A349277 _Seiichi Manyama_, Nov 12 2021