OFFSET
1,2
LINKS
Tewodros Amdeberhan, Moa Apagodu, and Doron Zeilberger, Wilf's "Snake Oil" Method Proves an Identity in The Motzkin Triangle, arXiv:1507.07660 [math.CO], 2015.
FORMULA
a(n) = Sum_{k=0..n} binomial(2*n, 2*k+1)*binomial(2*k+1, k)/(k+2), see Amdeberhan link. - Michel Marcus, Jul 29 2015
a(n) = n*hypergeom([1/2 - n, 1 - n], [3], 4). - Jean-François Alcover, Sep 22 2018
a(n) = A002026(2*n)/2. - Mark van Hoeij, Sep 05 2022
MAPLE
a := n -> n*hypergeom([1/2 - n, 1 - n], [3], 4);
seq(simplify(a(n)), n = 1..22); # Peter Luschny, Sep 05 2022
MATHEMATICA
a[n_] := n Hypergeometric2F1[1/2-n, 1-n, 3, 4]; Array[a, 22] (* Jean-François Alcover, Sep 22 2018 *)
PROG
(PARI) a(n) = sum(k=0, n, binomial(2*n, 2*k+1)*binomial(2*k+1, k)/(k+2)); \\ Michel Marcus, Jul 29 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Michel Marcus, Jul 29 2015
STATUS
approved