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%I #25 May 06 2022 13:13:51
%S 1,2,3,24,5,1800,7,15680,756,113400,11,79693891200,13,4372368,
%T 20495475,44972928000,17,2028339316523520,19,52737518268864000,
%U 3247700400,3585005424,23,38135556819759802035135799296,1328250,87885070000,370142004375,10293527616645873600000,29
%N a(n) = Product_{d|n} binomial(n,d).
%H Seiichi Manyama, <a href="/A308943/b308943.txt">Table of n, a(n) for n = 1..419</a>
%F a(n) = Product_{k=1..n} binomial(n,gcd(n,k))^(1/phi(n/gcd(n,k))) = Product_{k=1..n} binomial(n,n/gcd(n,k))^(1/phi(n/gcd(n,k))) where phi = A000010. - _Richard L. Ollerton_, Nov 08 2021
%t Table[Product[Binomial[n, d], {d, Divisors[n]}], {n, 1, 29}]
%o (PARI) a(n) = my(p=1); fordiv(n, d, p *= binomial(n, d)); p; \\ _Michel Marcus_, Jul 02 2019
%Y Cf. A001142, A008578 (fixed points), A056045 (similar, with Sum), A098710, A135396.
%Y Cf. A000010 (comments on product formulas).
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Jul 01 2019
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