A215251 Product of terms in n-th row of A037306.

1, 1, 1, 2, 4, 36, 225, 7840, 313600, 45302400, 8930250000, 8373836401920, 9001015156742400, 41813367543204433176, 325385777102562972821025, 8270190445766978650521600000, 377177413291384771899817984000000, 62187743659065606074696974956949929984

Offset: 1

Author

N. J. A. Sloane, Sep 05 2012

Keywords

• nonn
• easy

Comments

Also products of terms in rows of A047996.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..50
• R. Bekes, J. Pedersen and B. Shao, Mad tea party cyclic partitions, College Math. J., 43 (2012), 24-36.

Crossrefs

Cf. A037306, A008965, A047996.

Programs

Maple

with (numtheory):
a:= n-> mul (add(phi(d)*binomial(n/d, k/d),
                     d=divisors(igcd(n, k))), k=0..n)/n^(n+1):
seq (a(n), n=1..20);  # Alois P. Heinz, Sep 06 2012

Mathematica

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 *)