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Denominator of Product_{k=1..n} H(k), where H(k) = Sum_{j=1..k} 1/j, the k-th harmonic number.
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%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