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A363838 a(n) = Product_{b=2..n} b^gamma(n, b) where gamma(n, b) = Sum_{i>=1} floor(n/b^i).

%I A363838 #41 Oct 22 2023 01:50:12
%S A363838 1,1,2,6,96,480,17280,120960,30965760,2508226560,250822656000,
%T A363838 2759049216000,9535274090496000,123958563176448000,
%U A363838 24295878382583808000,5466572636081356800000,179128652139113899622400000,3045187086364936293580800000,53278593263040925392489676800000
%N A363838 a(n) = Product_{b=2..n} b^gamma(n, b) where gamma(n, b) = Sum_{i>=1} floor(n/b^i).
%C A363838 Generalized factorials.
%H A363838 Michel Marcus, <a href="/A363838/b363838.txt">Table of n, a(n) for n = 0..100</a>
%H A363838 Jeffrey C. Lagarias and Wijit Yangjit, <a href="https://arxiv.org/abs/2310.12949">The factorial function and generalizations, extended</a>, arXiv:2310.12949 [math.NT], 2023. See Section 7.2 p. 20 and Table 2 p. 29.
%o A363838 (PARI) f(n, b) = sum(i=1, logint(n, b), n\b^i);
%o A363838 a(n) = prod(b=2, n, b^f(n,b));
%o A363838 (Python)
%o A363838 from math import prod
%o A363838 from sympy import integer_log
%o A363838 def A363838(n): return prod(b**sum(n//b**i for i in range(1,integer_log(n,b)[0]+1)) for b in range(2,n+1)) # _Chai Wah Wu_, Oct 20 2023
%Y A363838 Row products of A153216.
%K A363838 nonn
%O A363838 0,3
%A A363838 _Michel Marcus_, Oct 20 2023