A367492 a(n) = Product_{k=0..n} (k+1)!^k.

1, 2, 72, 995328, 206391214080000, 39934999921327865856000000000, 654541076770994951831125144608178176000000000000000, 113391518341540395635327816456127297986876881699306137641287680000000000000000000000

Offset: 0

Author

Vaclav Kotesovec, Nov 20 2023

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..15

Crossrefs

Cf. A203421, A255269.

Programs

Magma

[(&*[Factorial(k+1)^k: k in [0..n]]): n in [0..15]]; // G. C. Greubel, Feb 18 2024

Mathematica

Table[Product[(k+1)!^k, {k, 0, n}], {n, 0, 10}]

SageMath

[product(factorial(k+1)^k for k in range(n+1)) for n in range(16)] # G. C. Greubel, Feb 18 2024

Formula

a(n) ~ A^(3/2) * n^(n^3/3 + 5*n^2/4 + 11*n/12 - 3/8) * (2*Pi)^(n^2/4 + n/4 - 1/2) / exp(4*n^3/9 + 7*n^2/8 - n + zeta(3)/(8*Pi^2) - 25/24), where A is the Glaisher-Kinkelin constant A074962.

a(n) = (n+1)^n * abs(A203421(n)) * A255269(n).