A026940 a(n) = Sum_{k=0..n-1} T(n,k) * T(n,k+1), with T given by A026300.

1, 6, 38, 256, 1805, 13162, 98469, 751656, 5831451, 45847770, 364498596, 2925337352, 23668977163, 192859753310, 1581188102590, 13034447714688, 107971181472779, 898274382703314, 7502546644142842, 62884859093960160, 528788663216036559, 4459599092506030110

Offset

1,2

Links

Table of n, a(n) for n=1..22.

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

Cf. A002026, A026300.

Sequence in context: A147957 A098410 A079949 * A082427 A192941 A263855

Adjacent sequences: A026937 A026938 A026939 * A026941 A026942 A026943

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Michel Marcus, Jul 29 2015

Status

approved