A146534 a(n) = 4*C(2n,n) - 3*0^n.

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

Links

Table of n, a(n) for n=0..26.

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 *)

Crossrefs

Cf. A000984, A001622, A010688, A029609, A029651, A039599, A088218, A100320, A144706, A146533, A240530.

Sequence in context: A179609 A241690 A141317 * A180888 A296400 A297808

Adjacent sequences: A146531 A146532 A146533 * A146535 A146536 A146537

Keyword

nonn,easy

Author

Philippe Deléham, Oct 31 2008

Extensions

a(22)-a(26) from Stefano Spezia, Feb 14 2025

Status

approved