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A143333 Pascal's triangle binomial(n,m) read by rows, all even elements replaced by zero.

%I A143333 #22 Dec 17 2015 02:57:44
%S A143333 1,1,1,1,0,1,1,3,3,1,1,0,0,0,1,1,5,0,0,5,1,1,0,15,0,15,0,1,1,7,21,35,
%T A143333 35,21,7,1,1,0,0,0,0,0,0,0,1,1,9,0,0,0,0,0,0,9,1,1,0,45,0,0,0,0,0,45,
%U A143333 0,1
%N A143333 Pascal's triangle binomial(n,m) read by rows, all even elements replaced by zero.
%C A143333 Row sums are A088560.
%C A143333 A047999(n,k) = A057427(T(n,k)). - _Reinhard Zumkeller_, Oct 24 2010
%H A143333 Reinhard Zumkeller, <a href="/A143333/b143333.txt">Rows n = 0..127 of triangle, flattened</a>
%H A143333 <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>
%F A143333 T(n,m) = A047999(n,m)*A007318(n,m).
%e A143333 The triangle starts in row n=0 with columns 0<=m<=n as:
%e A143333   1;
%e A143333   1,  1;
%e A143333   1,  0,  1;
%e A143333   1,  3,  3,  1;
%e A143333   1,  0,  0,  0,  1;
%e A143333   1,  5,  0,  0,  5,  1;
%e A143333   1,  0, 15,  0, 15,  0,  1;
%e A143333   1,  7, 21, 35, 35, 21,  7,  1;
%e A143333   1,  0,  0,  0,  0,  0,  0,  0,  1;
%e A143333   1,  9,  0,  0,  0,  0,  0,  0,  9,  1;
%e A143333   1,  0, 45,  0,  0,  0,  0,  0, 45,  0,  1;
%t A143333 t[n_, m_] = Mod[Binomial[n, m], 2]*Binomial[n, m]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]
%o A143333 (Haskell)
%o A143333 a143333 n k = a143333_tabl !! (n-1) !! (k-1)
%o A143333 a143333_row n = a143333_tabl !! (n-1)
%o A143333 a143333_tabl = zipWith(zipWith (*)) a007318_tabl a047999_tabl
%o A143333 -- _Reinhard Zumkeller_, Oct 10 2013
%Y A143333 Cf. A007318, A014421, A047999, A088560. - _Reinhard Zumkeller_, Oct 24 2010
%K A143333 nonn,tabl,easy,look
%O A143333 0,8
%A A143333 _Roger L. Bagula_ and _Gary W. Adamson_, Oct 21 2008
%E A143333 Offset set to 0 by _Reinhard Zumkeller_, Oct 21 2010