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%I #10 Mar 11 2021 07:28:52
%S 1,-1,1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,1,-1,-1,1,-1,1,1,-1,-1,1,1,-1,1,
%T -1,-1,1,-1,1,1,-1,1,-1,-1,1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,
%U -1,1,1,-1,1,-1,-1,1,1,-1,-1,1,-1,1,1,-1,-1,1,1
%N T(0,0) = 1, T(n+1,2*k) = - T(n,k), T(n+1,2*k+1) = T(n,k), k=0..n, triangle read by rows.
%C Row n has 2^n terms;
%C sum of row n = 0 for n > 0, cf. A000007;
%C numerator of Bernoulli tree, see Woon link; denominators = A106831.
%H Reinhard Zumkeller, <a href="/A242179/b242179.txt">Rows n = 0..12 of table, flattened</a>
%H S. C. Woon, <a href="http://www.jstor.org/stable/2691054">A tree for generating Bernoulli numbers</a>, Math. Mag., 70 (1997), 51-56.
%H <a href="/index/Be#Bernoulli">Index entries for sequences related to Bernoulli Numbers.</a>
%o (Haskell)
%o a242179 n k = a242179_tabf !! n !! n
%o a242179_row n = a242179_tabf !! n
%o a242179_tabf = iterate (concatMap (\x -> [-x, x])) [1] :: (Num t => [[t]])
%o a242179_list = concat a242179_tabf
%o (PARI) T(n,k) = (-1)^(n - hammingweight(k));
%o a(n) = n++; -(-1)^(logint(n,2) - hammingweight(n)); \\ _Kevin Ryde_, Mar 11 2021
%Y Cf. A059448 (values 0,1), A298952 (values 1,0).
%Y Cf. A106831, A060054, A075180, A164555, A027642.
%K sign,tabf,frac
%O 0
%A _Reinhard Zumkeller_, Jul 04 2014
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