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A360604 Triangle read by rows. T(n, k) = 2^binomial(n - k, 2) * binomial(n - 1, k - 1).

%I A360604 #4 Feb 23 2023 08:36:13
%S A360604 1,0,1,0,1,1,0,2,2,1,0,8,6,3,1,0,64,32,12,4,1,0,1024,320,80,20,5,1,0,
%T A360604 32768,6144,960,160,30,6,1,0,2097152,229376,21504,2240,280,42,7,1,0,
%U A360604 268435456,16777216,917504,57344,4480,448,56,8,1
%N A360604 Triangle read by rows. T(n, k) = 2^binomial(n - k, 2) * binomial(n - 1, k - 1).
%e A360604 Triangle T(n, k) starts:
%e A360604 [0] 1;
%e A360604 [1] 0,       1;
%e A360604 [2] 0,       1,      1;
%e A360604 [3] 0,       2,      2,     1;
%e A360604 [4] 0,       8,      6,     3,    1;
%e A360604 [5] 0,      64,     32,    12,    4,   1;
%e A360604 [6] 0,    1024,    320,    80,   20,   5,  1;
%e A360604 [7] 0,   32768,   6144,   960,  160,  30,  6, 1;
%e A360604 [8] 0, 2097152, 229376, 21504, 2240, 280, 42, 7, 1;
%p A360604 T := (n, k) -> 2^binomial(n - k, 2) * binomial(n-1, k-1):
%p A360604 for n from 0 to 9 do seq(T(n, k), k = 0..n) od;
%Y A360604 Cf. A006125 (column 1), A002378 (T(n+2,n)), A130809 (T(n+3,n)), A006896 (row sums).
%K A360604 nonn,tabl
%O A360604 0,8
%A A360604 _Peter Luschny_, Feb 23 2023