A384163 a(n) = Product_{k=0..n-1} (2*n+3*k).
1, 2, 28, 648, 20944, 869440, 44089920, 2641533440, 182573036800, 14299419214080, 1251598943795200, 121073405444992000, 12826824167930572800, 1477015178613438464000, 183679785389526871244800, 24533610049517447983104000, 3502810763000490499317760000, 532374290389646285405913088000
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
Crossrefs
Cf. A352601.
Programs
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Magma
[1] cat [&*[(2*n+3*k): k in [0..n-1]]: n in [1..16]]; // Vincenzo Librandi, May 22 2025
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Mathematica
a[n_]:=Product[(2*n+3*k),{k,0,n-1}]; Table[a[n],{n,0,15}] (* Vincenzo Librandi, May 22 2025 *) -
PARI
a(n) = prod(k=0, n-1, 2*n+3*k);
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Sage
def a(n): return 3^n*rising_factorial(2*n/3, n)
Formula
a(n) = 3^n * RisingFactorial(2*n/3,n).
a(n) = n! * [x^n] 1/(1 - 3*x)^(2*n/3).
a(n) = (2/5) * 3^n * n! * binomial(5*n/3,n) for n > 0.