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A367492 a(n) = Product_{k=0..n} (k+1)!^k. 1
1, 2, 72, 995328, 206391214080000, 39934999921327865856000000000, 654541076770994951831125144608178176000000000000000, 113391518341540395635327816456127297986876881699306137641287680000000000000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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).
MATHEMATICA
Table[Product[(k+1)!^k, {k, 0, n}], {n, 0, 10}]
PROG
(Magma) [(&*[Factorial(k+1)^k: k in [0..n]]): n in [0..15]]; // G. C. Greubel, Feb 18 2024
(SageMath) [product(factorial(k+1)^k for k in range(n+1)) for n in range(16)] # G. C. Greubel, Feb 18 2024
CROSSREFS
Sequence in context: A244148 A320443 A079478 * A221709 A036899 A324566
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Nov 20 2023
STATUS
approved

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Last modified April 16 08:27 EDT 2024. Contains 371698 sequences. (Running on oeis4.)