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