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

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

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.

a(n) ~ 5^(5*n/3-1/2) * (n/e)^n / 2^(2*n/3-1/2). - Amiram Eldar, Dec 27 2025

Mathematica

a[n_]:=Product[(2*n+3*k), {k, 0, n-1}]; Table[a[n], {n, 0, 15}] (* Vincenzo Librandi, May 22 2025 *)

Prog

(PARI) a(n) = prod(k=0, n-1, 2*n+3*k);
(SageMath)
def a(n): return 3^n*rising_factorial(2*n/3, n)
(Magma) [1] cat  [&*[(2*n+3*k): k in [0..n-1]]: n in [1..16]]; // Vincenzo Librandi, May 22 2025

Crossrefs

Cf. A352601.

Sequence in context: A326282 A373315 A246483 * A151332 A098631 A089836

Adjacent sequences: A384160 A384161 A384162 * A384164 A384165 A384166

Keyword

nonn,easy

Author

Seiichi Manyama, May 21 2025

Status

approved