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%I #9 Sep 08 2022 08:45:41
%S 1,0,2,-1,1,4,-2,-1,3,8,-3,-4,0,7,16,-4,-8,-6,3,15,32,-5,-13,-16,-7,
%T 10,31,64,-6,-19,-31,-27,-5,25,63,128,-7,-26,-52,-62,-40,4,56,127,256,
%U -8,-34,-80,-118,-110,-52,28,119,255,512,-9,-43,-116,-202,-236,-178,-56,83,246,511,1024
%N Triangle read by rows: T(n, k) = 2^k - binomial(n, k+1).
%C Row sums are 2^n: {1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, ...}
%H G. C. Greubel, <a href="/A156861/b156861.txt">Rows n = 0..100 of triangle, flattened</a>
%F T(n, k) = 2^k - binomial(n, k+1).
%F From _G. C. Greubel_, Nov 30 2019: (Start)
%F T(n, n) = 2^n.
%F Sum_{k=0..n-1} T(n,k) = 0. (End)
%e Triangle begins as:
%e 1;
%e 0, 2;
%e -1, 1, 4;
%e -2, -1, 3, 8;
%e -3, -4, 0, 7, 16;
%e -4, -8, -6, 3, 15, 32;
%e -5, -13, -16, -7, 10, 31, 64;
%e -6, -19, -31, -27, -5, 25, 63, 128;
%e -7, -26, -52, -62, -40, 4, 56, 127, 256;
%e -8, -34, -80, -118, -110, -52, 28, 119, 255, 512;
%e -9, -43, -116, -202, -236, -178, -56, 83, 246, 511, 1024;
%p seq(seq( 2^k - binomial(n, k+1), k=0..n), n=0..10); # _G. C. Greubel_, Nov 30 2019
%t Table[2^k -Binomial[n, k+1], {n,0,10}, {k,0,n}]//Flatten
%o (PARI) T(n,k) = 2^k - binomial(n, k+1); \\ _G. C. Greubel_, Nov 30 2019
%o (Magma) [2^k - Binomial(n, k+1): k in [0..n], n in [0..10]]; // _G. C. Greubel_, Nov 30 2019
%o (Sage) [[2^k - binomial(n, k+1) for k in (0..n)] for n in (0..10)] # _G. C. Greubel_, Nov 30 2019
%o (GAP) Flat(List([0..10], n-> List([0..n], k-> 2^k - Binomial(n, k+1) ))); # _G. C. Greubel_, Nov 30 2019
%K sign,tabl
%O 0,3
%A _Roger L. Bagula_, Feb 17 2009
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