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A034871 Odd-numbered rows of Pascal's triangle. 5

%I

%S 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 36,9,1,1,11,55,165,330,462,462,330,165,55,11,1,1,13,78,286,715,1287,

%U 1716,1716,1287,715,286,78,13,1,1,15,105,455,1365,3003,5005

%N Odd-numbered rows of Pascal's triangle.

%H Eduardo H. M. Brietzke, <a href="http://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 G.f.: (1+y)/(1-x*(1+y)^2). - _Vladimir Kruchinin_, Nov 22 2020

%t Take[Table[Binomial[n,m],{n,0,20},{m,0,n}],{2,-1,2}]//Flatten (* _Harvey P. Dale_, Dec 10 2018 *)

%o (Haskell)

%o a034871 n = a034871_list !! n

%o a034871_list = concat $ map ([1,1] ^) [1,3..]

%o instance Num a => Num [a] where

%o fromInteger k = [fromInteger k]

%o (p:ps) + (q:qs) = p + q : ps + qs

%o ps + qs = ps ++ qs

%o (p:ps) * qs'@(q:qs) = p * q : ps * qs' + [p] * qs

%o _ * _ = []

%o -- _Reinhard Zumkeller_, Apr 02 2011

%Y Cf. A007318, A034870.

%K nonn,tabf,easy

%O 0,4

%A _N. J. A. Sloane_.

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Last modified May 13 05:02 EDT 2021. Contains 343836 sequences. (Running on oeis4.)