A386393 Triangle T(n, k) (1 <= k <= n) read by rows: T(n, k) is the numerator of R(n, k) where R(n, k) = R(n, k-1)/2 + R(n-1, k-1) for 1 < k <= n with R(n, 1) = R(n-1, n-1) for n > 1, R(1, 1) = 1.

1, 1, 3, 3, 7, 19, 19, 43, 99, 251, 251, 555, 1243, 2827, 6843, 6843, 14875, 32635, 72411, 162875, 381851, 381851, 819803, 1771803, 3860443, 8494747, 18918747, 43357211, 43357211, 92234139, 197168923, 423959707, 918096411, 2005424027, 4427023643, 9976746651

Offset: 1

Author

Mikhail Kurkov, Jul 20 2025

Keywords

• nonn
• tabl
• frac

Comments

Denominator of R(n, k) is 2^((n-1)*(n-2)/2+k-1).

Examples

			Triangle begins:
       1;
       1,      3;
       3,      7,      19;
      19,     43,      99,     251;
     251,    555,    1243,    2827,    6843;
    6843,  14875,   32635,   72411,  162875,   381851;
  381851, 819803, 1771803, 3860443, 8494747, 18918747, 43357211;
		

Crossrefs

Cf. A305562.

Programs

PARI

rows_upto(n) = {my(A, v1, v2, v3);
v1 = vector(n, i, 0); v1[1] = 1;
v2 = vector(n, i, 0); v2[1] = [1];
for(i=2, n, v3 = v1; v1[1] = v3[i-1];
for(j=2, i, v1[j] = v1[j-1]/2 + v3[j-1]);
A = 2^((i-1)*(i-2)/2);
v2[i] = vector(i, j, A*2^(j-1)*v1[j])); v2}