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A034871 Odd-numbered rows of Pascal's triangle.

%I A034871 #20 Jul 08 2025 21:28:09
%S A034871 1,1,1,3,3,1,1,5,10,10,5,1,1,7,21,35,35,21,7,1,1,9,36,84,126,126,84,
%T A034871 36,9,1,1,11,55,165,330,462,462,330,165,55,11,1,1,13,78,286,715,1287,
%U A034871 1716,1716,1287,715,286,78,13,1,1,15,105,455,1365,3003,5005
%N A034871 Odd-numbered rows of Pascal's triangle.
%H A034871 Eduardo H. M. Brietzke, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/44-2/quarteduardobrietzke02_2006.pdf">Generalization of an identity of Andrews</a>, Fibonacci Quart. 44 (2006), no. 2, 166-171.
%F A034871 G.f.: (1+y)/(1-x*(1+y)^2). - _Vladimir Kruchinin_, Nov 22 2020
%t A034871 Take[Table[Binomial[n,m],{n,0,20},{m,0,n}],{2,-1,2}]//Flatten (* _Harvey P. Dale_, Dec 10 2018 *)
%o A034871 (Haskell)
%o A034871 a034871 n = a034871_list !! n
%o A034871 a034871_list = concat $ map ([1,1] ^) [1,3..]
%o A034871 instance Num a => Num [a] where
%o A034871    fromInteger k = [fromInteger k]
%o A034871    (p:ps) + (q:qs) = p + q : ps + qs
%o A034871    ps + qs         = ps ++ qs
%o A034871    (p:ps) * qs'@(q:qs) = p * q : ps * qs' + [p] * qs
%o A034871    _ * _               = []
%o A034871 -- _Reinhard Zumkeller_, Apr 02 2011
%Y A034871 Cf. A007318, A034870.
%K A034871 nonn,tabf,easy
%O A034871 0,4
%A A034871 _N. J. A. Sloane_