A097423 - OEIS

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A097423

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

1, 3, 11, 275, 7535, 73843, 1276429, 138766067, 989263291643, 7301752355616983, 55566999221913933083, 434538985460750767066613, 3482368080874980096524258963, 28534304884670510863221395297153

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..14.

EXAMPLE

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

MATHEMATICA

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

Numerator[Rest[FoldList[Times, 1, HarmonicNumber[Range[20]]]]] (* Harvey P. Dale, Apr 02 2015 *)

PROG

(PARI) hh(n)=sum(i=1, n, 1/i); ff(n)=numerator(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. A097424.

Sequence in context: A112357 A205771 A373342 * A111130 A337415 A264725

Adjacent sequences: A097420 A097421 A097422 * A097424 A097425 A097426

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