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

0,4

Links

Table of n, a(n) for n=0..62.

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

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A007318, A034870.

Sequence in context: A196493 A251634 A196989 * A333758 A015109 A319699

Adjacent sequences: A034868 A034869 A034870 * A034872 A034873 A034874

Keyword

nonn,tabf,easy

Author

N. J. A. Sloane.

Status

approved