A384165 a(n) = Product_{k=0..n-1} (3*n+2*k).
1, 3, 48, 1287, 48384, 2340135, 138378240, 9672183675, 780151357440, 71322093677835, 7287813911347200, 823100991923184975, 101819334240239616000, 13690816766440373134575, 1988199345147516813312000, 310120801435080997013527875, 51709528644340997758648320000
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
Programs
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Magma
[1] cat [&*[(3*n + 2*k): k in [0..n-1]]: n in [1..16]]; // Vincenzo Librandi, May 22 2025
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Mathematica
a[n_]:=Product[(3*n+2*k),{k,0,n-1}]; Table[a[n],{n,0,15}] (* Vincenzo Librandi, May 22 2025 *) -
PARI
a(n) = prod(k=0, n-1, 3*n+2*k);
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Python
from math import prod def A384165(n): return prod(3*n+i for i in range(0,n<<1,2)) # Chai Wah Wu, May 21 2025
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Sage
def a(n): return 2^n*rising_factorial(3*n/2, n)
Formula
a(n) = 2^n * RisingFactorial(3*n/2,n).
a(n) = n! * [x^n] 1/(1 - 2*x)^(3*n/2).
a(n) = (3/5) * 2^n * n! * binomial(5*n/2,n) for n > 0.