A384263 a(n) = Product_{k=0..n-1} (3*n+k-1).
1, 2, 30, 720, 24024, 1028160, 53721360, 3315312000, 235989936000, 19033511777280, 1715456253772800, 170866312333516800, 18638248113733248000, 2209723830420986880000, 282926061171849199104000, 38906746608339829739520000, 5719086709283091520696320000, 894889312443445445244518400000
Offset: 0
Programs
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Mathematica
a[n_]:=n!*Binomial[4*n-2,n]; Array[a,18,0] (* Stefano Spezia, Sep 04 2025 *)
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PARI
a(n) = prod(k=0, n-1, 3*n+k-1);
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Python
from sympy import rf def a(n): return rf(3*n-1, n)
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Sage
def a(n): return rising_factorial(3*n-1, n)
Formula
a(n) = RisingFactorial(3*n-1,n).
a(n) = n! * [x^n] 1/(1 - x)^(3*n-1).
a(n) = n! * binomial(4*n-2,n).
From Stefano Spezia, Sep 04 2025: (Start)
E.g.f.: (1 + 3*hypergeom([-1/4, 1/4, 1/2], [-1/3, 1/3], 2^8*x/3^3])/4.
a(n) ~ 2^(8*n-7)*3^(-3*n-1/2)*exp(-n)*n^(n-1)*(144*n - 13). (End)