A082688
Denominator of Sum_{k=1..n} 1/(n+k).
Original entry on oeis.org
2, 12, 60, 840, 2520, 27720, 360360, 144144, 2450448, 232792560, 232792560, 5354228880, 26771144400, 11473347600, 332727080400, 20629078984800, 20629078984800, 144403552893600, 5342931457063200, 5342931457063200
Offset: 1
1/2, 7/12, 37/60, 533/840, 1627/2520, 18107/27720, 237371/360360, ...
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Table[HarmonicNumber[2 n] - HarmonicNumber[n], {n, 20}] // Denominator (* Eric W. Weisstein, Dec 14 2017 *)
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a(n) = denominator(sum(k=1, n, 1/(n+k))); \\ Michel Marcus, Dec 14 2017
A250344
Numerator of the harmonic mean of the first n hexagonal numbers.
Original entry on oeis.org
1, 12, 90, 1680, 6300, 83160, 1261260, 576576, 11027016, 1163962800, 1280359080, 32125373280, 174012438600, 80313433200, 2495453103000, 165032631878400, 175347171370800, 1299631976042400, 50757848842100400, 53429314570632000, 2300131992265707600
Offset: 1
a(3) = 90 because the first 3 hexagonal numbers are [1,6,15], and 3/(1/1+1/6+1/15) = 90/37.
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harmonicmean(v) = #v / sum(k=1, #v, 1/v[k])
s=vector(30); for(n=1, #s, s[n]=numerator(harmonicmean(vector(n, k, k*(2*k-1))))); s
A129764
Numerator of the sum of all elements of n X n X n cubic array M[i,j,k] = 1/(i+j+k-2).
Original entry on oeis.org
1, 15, 1133, 1177, 129149, 349673, 57087959, 345322023, 14272692271, 40165727117, 217549734472087, 14553241481573, 18901300532988407, 40603763694792631, 9565202506169243753, 63888449105310899
Offset: 1
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Table[ Numerator[ Sum[ Sum[ Sum[ 1/(i+j+k-2), {i,1,n} ], {j,1,n} ], {k,1,n} ] ], {n,1,30} ]
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