A286033 a(n) = binomial(2*n-2, n-1) + (-1)^n.

0, 3, 5, 21, 69, 253, 923, 3433, 12869, 48621, 184755, 705433, 2704155, 10400601, 40116599, 155117521, 601080389, 2333606221, 9075135299, 35345263801, 137846528819, 538257874441, 2104098963719, 8233430727601, 32247603683099, 126410606437753, 495918532948103

Offset

1,2

Comments

An odd prime p divides a((p+1)/2) which gives A163210.

Links

Table of n, a(n) for n=1..27.

Formula

a(n) = A000984(n-1) + A033999(n). - David A. Corneth, May 13 2017

G.f.: -1 + x/sqrt(1 - 4*x) + 1/(1 + x). - Ilya Gutkovskiy, May 13 2017

D-finite with recurrence: (-n+1)*a(n) +2*(n-1)*a(n-1) +(7*n-17)*a(n-2) +2*(2*n-7)*a(n-3)=0. - R. J. Mathar, Jan 27 2020

Maple

a := n -> binomial(2*n-2, n-1) + (-1)^n: seq(a(n), n=1..27);

Mathematica

a[n_] := Binomial[2n-2, n-1] + (-1)^n); a[Range[1, 27]]

Prog

(PARI) a(n) = binomial(2*n-2, n-1) + (-1)^n \\ David A. Corneth, May 13 2017

Crossrefs

Cf. A163210, A178904, A219539.

Sequence in context: A153862 A266203 A264683 * A056803 A071706 A196418

Adjacent sequences: A286030 A286031 A286032 * A286034 A286035 A286036

Keyword

nonn,easy

Author

Peter Luschny, May 13 2017

Status

approved