cp's OEIS Frontend

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.

%I A386393 #6 Jul 21 2025 01:44:55
%S A386393 1,1,3,3,7,19,19,43,99,251,251,555,1243,2827,6843,6843,14875,32635,
%T A386393 72411,162875,381851,381851,819803,1771803,3860443,8494747,18918747,
%U A386393 43357211,43357211,92234139,197168923,423959707,918096411,2005424027,4427023643,9976746651
%N 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.
%C A386393 Denominator of R(n, k) is 2^((n-1)*(n-2)/2+k-1).
%e A386393 Triangle begins:
%e A386393        1;
%e A386393        1,      3;
%e A386393        3,      7,      19;
%e A386393       19,     43,      99,     251;
%e A386393      251,    555,    1243,    2827,    6843;
%e A386393     6843,  14875,   32635,   72411,  162875,   381851;
%e A386393   381851, 819803, 1771803, 3860443, 8494747, 18918747, 43357211;
%o A386393 (PARI) rows_upto(n) = {my(A, v1, v2, v3);
%o A386393 v1 = vector(n, i, 0); v1[1] = 1;
%o A386393 v2 = vector(n, i, 0); v2[1] = [1];
%o A386393 for(i=2, n, v3 = v1; v1[1] = v3[i-1];
%o A386393 for(j=2, i, v1[j] = v1[j-1]/2 + v3[j-1]);
%o A386393 A = 2^((i-1)*(i-2)/2);
%o A386393 v2[i] = vector(i, j, A*2^(j-1)*v1[j])); v2}
%Y A386393 Cf. A305562.
%K A386393 nonn,tabl,frac
%O A386393 1,3
%A A386393 _Mikhail Kurkov_, Jul 20 2025