A124862 a(n) = J(2*n+1) * C(2*n,n), where J(n) = A001045(n).

1, 6, 66, 860, 11970, 172116, 2523444, 37487736, 562303170, 8496977060, 129153866556, 1972531074696, 30245473774516, 465314970745800, 7179145222818600, 111037445957810160, 1721080411744977090, 26727366391823685060, 415759032752626632300, 6477088089163469639400

Offset

0,2

Comments

Central coefficients of number triangle A124860.

Links

Table of n, a(n) for n=0..19.

Formula

From Amiram Eldar, Jan 24 2026: (Start)

a(n) = A007583(n) * A000984(n).

G.f.: (2/sqrt(1-16*x) + 1/sqrt(1-4*x)) / 3.

E.g.f.: (exp(2*x) * BesselI(0, 2*x) + 2 * exp(8*x) * BesselI(0, 8*x)) / 3. (End)

Mathematica

a[n_] := Binomial[2*n, n]*(2^(2*n+1) + 1)/3; Array[a, 20, 0] (* Amiram Eldar, Jan 24 2026 *)

Crossrefs

Cf. A000984, A001045, A007583, A124860.

Sequence in context: A004355 A282046 A382364 * A130977 A191096 A151832

Adjacent sequences: A124859 A124860 A124861 * A124863 A124864 A124865

Keyword

easy,nonn

Author

Paul Barry, Nov 10 2006

Extensions

More terms from Amiram Eldar, Jan 24 2026

Status

approved