A384166 a(n) = Product_{k=0..n-1} (3*n+4*k).
1, 3, 60, 1989, 92160, 5486535, 399072960, 34298042625, 3400783626240, 382128386114475, 47986411423104000, 6659996213472126525, 1012334387351519232000, 167253493686752981883375, 29842935065036371998720000, 5719198821953333723419037625, 1171620424982972483984424960000
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
Programs
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Magma
[1] cat [&*[(3*n + 4*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+4*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+4*k);
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Python
from math import prod def A384166(n): return prod(3*n+i for i in range(0,n<<2,4)) # Chai Wah Wu, May 21 2025
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Sage
def a(n): return 4^n*rising_factorial(3*n/4, n)
Formula
a(n) = 4^n * RisingFactorial(3*n/4,n).
a(n) = n! * [x^n] 1/(1 - 4*x)^(3*n/4).
a(n) = (3/7) * 4^n * n! * binomial(7*n/4,n) for n > 0.