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A136501 Triangle, read by rows, where T(n,k) = C(2^k,n-k) for n>=k>=0.

%I A136501 #6 Mar 15 2021 01:55:59
%S A136501 1,1,1,0,2,1,0,1,4,1,0,0,6,8,1,0,0,4,28,16,1,0,0,1,56,120,32,1,0,0,0,
%T A136501 70,560,496,64,1,0,0,0,56,1820,4960,2016,128,1,0,0,0,28,4368,35960,
%U A136501 41664,8128,256,1,0,0,0,8,8008,201376,635376,341376,32640,512,1,0,0,0,1,11440,906192,7624512,10668000,2763520,130816,1024,1
%N A136501 Triangle, read by rows, where T(n,k) = C(2^k,n-k) for n>=k>=0.
%H A136501 G. C. Greubel, <a href="/A136501/b136501.txt">Rows n = 0..50 of the triangle, flattened</a>
%e A136501 Triangle begins:
%e A136501   1;
%e A136501   1, 1;
%e A136501   0, 2, 1;
%e A136501   0, 1, 4,  1;
%e A136501   0, 0, 6,  8,     1;
%e A136501   0, 0, 4, 28,    16,      1;
%e A136501   0, 0, 1, 56,   120,     32,       1;
%e A136501   0, 0, 0, 70,   560,    496,      64,        1;
%e A136501   0, 0, 0, 56,  1820,   4960,    2016,      128,       1;
%e A136501   0, 0, 0, 28,  4368,  35960,   41664,     8128,     256,      1;
%e A136501   0, 0, 0,  8,  8008, 201376,  635376,   341376,   32640,    512,    1;
%e A136501   0, 0, 0,  1, 11440, 906192, 7624512, 10668000, 2763520, 130816, 1024, 1;
%t A136501 Table[Binomial[2^k, n-k], {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, Mar 15 2021 *)
%o A136501 (PARI) T(n,k)=binomial(2^k,n-k)
%o A136501 (Magma) [Binomial(2^k, n-k): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Mar 15 2021
%o A136501 (Sage) flatten([[binomial(2^k, n-k) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Mar 15 2021
%Y A136501 Cf. A014070 (central terms), A121688 (row sums), A136502 (matrix inverse).
%K A136501 nonn,tabl
%O A136501 0,5
%A A136501 _Paul D. Hanna_, Jan 01 2008