A034871 Odd-numbered rows of Pascal's triangle.

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, 36, 9, 1, 1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1, 1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1, 1, 15, 105, 455, 1365, 3003, 5005

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• tabf
• easy

Links

• Eduardo H. M. Brietzke, Generalization of an identity of Andrews, Fibonacci Quart. 44 (2006), no. 2, 166-171.

Crossrefs

Cf. A007318, A034870.

Programs

Haskell

a034871 n = a034871_list !! n
a034871_list = concat $ map ([1,1] ^) [1,3..]
instance Num a => Num [a] where
   fromInteger k = [fromInteger k]
   (p:ps) + (q:qs) = p + q : ps + qs
   ps + qs         = ps ++ qs
   (p:ps) * qs'@(q:qs) = p * q : ps * qs' + [p] * qs
    *                = []
-- Reinhard Zumkeller, Apr 02 2011

Mathematica

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

Formula

G.f.: (1+y)/(1-x*(1+y)^2). - Vladimir Kruchinin, Nov 22 2020