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A286033
a(n) = binomial(2*n-2, n-1) + (-1)^n.
2
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
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
(Magma) [Binomial(2*n-2, n-1) + (-1)^n: n in [1..30]]; // G. C. Greubel, Jul 14 2024
(SageMath)
def A286033(n): return binomial(2*n-2, n-1) + (-1)^n
[A286033(n) for n in range(1, 31)] # G. C. Greubel, Jul 14 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Luschny, May 13 2017
STATUS
approved