A386876 a(n) = (1/2) * (3*n)! / n!^3 for n > 0, a(0) = 1.

1, 3, 45, 840, 17325, 378378, 8576568, 199536480, 4732755885, 113936715750, 2775498395670, 68263497731520, 1692365881260600, 42239049036433200, 1060286332955364000, 26747489892687315840, 677672732203007541165, 17234929348415589714750, 439809863742901530128250

Offset: 0

Author

Peter Luschny, Aug 06 2025

Keywords

• nonn
• easy

Links

• Paolo Xausa, Table of n, a(n) for n = 0..650

Crossrefs

Cf. A006480, A386789.

Programs

Maple

egf := (1 + hypergeom([1/3, 2/3], [1, 1], 27*x)) / 2:
ser := series(egf, x, 20): seq(n!*coeff(ser, x, n), n = 0.. 18);

Mathematica

A386876[n_] := Binomial[2*n - 1, n - 1]*Binomial[3*n, n];
Array[A386876, 20, 0] (* Paolo Xausa, Aug 06 2025 *)

Formula

a(n) = binomial(2*n - 1, n - 1)*binomial(3*n, n).

a(n) = n! * [x^n] (1 + hypergeom([1/3, 2/3], [1, 1], 27*x)) / 2.

a(n) ~ 3^(3*n+1/2)/(4*n*Pi). - Stefano Spezia, Aug 06 2025