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URL: https://oeis.org/A146534

⇱ A146534 - OEIS

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A146534
a(n) = 4*C(2n,n) - 3*0^n.
2
1, 8, 24, 80, 280, 1008, 3696, 13728, 51480, 194480, 739024, 2821728, 10816624, 41602400, 160466400, 620470080, 2404321560, 9334424880, 36300541200, 141381055200, 551386115280, 2153031497760, 8416395854880, 32933722910400, 128990414732400, 505642425751008, 1983674131792416
OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..n} A039599(n,k)*A010688(k).
From Stefano Spezia, Feb 14 2025: (Start)
G.f.: 4/sqrt(1 - 4*x) - 3.
E.g.f.: 4*exp(2*x)*BesselI(0, 2*x) - 3. (End)
From Amiram Eldar, Oct 18 2025: (Start)
Sum_{n>=0} 1/a(n) = 13/12 + Pi/(18*sqrt(3)).
Sum_{n>=0} (-1)^n/a(n) = 19/20 - log(phi)/(5*sqrt(5)), where phi is the golden ratio (A001622). (End)
MATHEMATICA
a[n_]:=4*Binomial[2n, n]-3*KroneckerDelta[n, 0]; Array[a, 27, 0] (* Stefano Spezia, Feb 14 2025 *)
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Oct 31 2008
EXTENSIONS
a(22)-a(26) from Stefano Spezia, Feb 14 2025
STATUS
approved