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%I #17 May 24 2023 07:33:35
%S 1,1,1,2,4,36,225,7840,313600,45302400,8930250000,8373836401920,
%T 9001015156742400,41813367543204433176,325385777102562972821025,
%U 8270190445766978650521600000,377177413291384771899817984000000,62187743659065606074696974956949929984
%N Product of terms in n-th row of A037306.
%C Also products of terms in rows of A047996.
%H Alois P. Heinz, <a href="/A215251/b215251.txt">Table of n, a(n) for n = 1..50</a>
%H R. Bekes, J. Pedersen and B. Shao, <a href="https://www.jstor.org/stable/10.4169/college.math.j.43.1.025">Mad tea party cyclic partitions</a>, College Math. J., 43 (2012), 24-36.
%p with (numtheory):
%p a:= n-> mul (add(phi(d)*binomial(n/d, k/d),
%p d=divisors(igcd(n, k))), k=0..n)/n^(n+1):
%p seq (a(n), n=1..20); # _Alois P. Heinz_, Sep 06 2012
%t t[n_, k_] := Total[EulerPhi[#] * Binomial[n/#, k/#]& /@ Divisors[GCD[n, k]]]/n; Table[Times @@ Table[t[n, k], {k, 1, n}], {n, 1, 18}] (* _Jean-François Alcover_, Mar 07 2014 *)
%Y Cf. A037306, A008965, A047996.
%K nonn,easy
%O 1,4
%A _N. J. A. Sloane_, Sep 05 2012
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