%I #14 Mar 28 2015 22:37:14
%S 1,2,4,48,576,2304,15360,614400,1548288000,3901685760000,
%T 9832248115200000,24777265250304000000,62438708430766080000000,
%U 157345545245530521600000000,5154640062243579887616000000000
%N Denominator of Product_{k=1..n} H(k), where H(k) = Sum_{j=1..k} 1/j, the k-th harmonic number.
%e (1)(1 + 1/2)(1 + 1/2 + 1/3) = 1*(3/2)*(11/6) = 11/4, so a(3) = 4.
%t a[n_] := Denominator[ Product[ HarmonicNumber[k], {k, 1, n}]]; Table[ a[n], {n, 14}] (* _Robert G. Wilson v_, Aug 26 2004 *)
%o (PARI) hh(n)=sum(i=1,n,1/i); ff(n)=denominator(prod(i=1,n,hh(i))); for (i=1,30,print1(ff(i),",")) \\ Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Aug 23 2004
%Y Cf. A097423.
%K frac,nonn
%O 1,2
%A _Leroy Quet_, Aug 21 2004
%E More terms from Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com) and _Robert G. Wilson v_, Aug 23 2004