A097424 Denominator of Product_{k=1..n} H(k), where H(k) = Sum_{j=1..k} 1/j, the k-th harmonic number.

1, 2, 4, 48, 576, 2304, 15360, 614400, 1548288000, 3901685760000, 9832248115200000, 24777265250304000000, 62438708430766080000000, 157345545245530521600000000, 5154640062243579887616000000000

Offset

1,2

Links

Table of n, a(n) for n=1..15.

Example

(1)(1 + 1/2)(1 + 1/2 + 1/3) = 1*(3/2)*(11/6) = 11/4, so a(3) = 4.

Mathematica

a[n_] := Denominator[ Product[ HarmonicNumber[k], {k, 1, n}]]; Table[ a[n], {n, 14}] (* Robert G. Wilson v, Aug 26 2004 *)

Prog

(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

Crossrefs

Cf. A097423.

Sequence in context: A144578 A143968 A308665 * A228596 A032019 A181179

Adjacent sequences: A097421 A097422 A097423 * A097425 A097426 A097427

Keyword

frac,nonn

Author

Leroy Quet, Aug 21 2004

Extensions

More terms from Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com) and Robert G. Wilson v, Aug 23 2004

Status

approved