A384262 a(n) = Product_{k=0..n-1} (3*n+k-2).
1, 1, 20, 504, 17160, 742560, 39070080, 2422728000, 173059286400, 13995229248000, 1264020397516800, 126115611484262400, 13776096431889792000, 1635195634511530291200, 209574860127295703040000, 28844656968251942737920000, 4243193364951971128258560000, 664387519844376163893657600000
Offset: 0
Programs
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PARI
a(n) = prod(k=0, n-1, 3*n+k-2);
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Python
from sympy import rf def a(n): return rf(3*n-2, n)
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Sage
def a(n): return rising_factorial(3*n-2, n)
Formula
a(n) = RisingFactorial(3*n-2,n).
a(n) = n! * [x^n] 1/(1 - x)^(3*n-2).
a(n) = n! * binomial(4*n-3,n).
D-finite with recurrence 3*(3*n-4)*(3*n-5)*a(n) -8*(4*n-5)*(4*n-3)*(2*n-3)*a(n-1)=0. - R. J. Mathar, May 26 2025