A353250 a(0) = 1, a(n) = harmonic_mean(a(n-1), n), where harmonic_mean(p, q) = 2/(1/p + 1/q); numerators.
1, 1, 4, 24, 48, 480, 960, 13440, 26880, 161280, 322560, 7096320, 14192640, 369008640, 738017280, 295206912, 590413824, 20074070016, 40148140032, 1525629321216, 15256293212160, 30512586424320, 61025172848640, 2807157951037440, 5614315902074880
Offset: 0
Examples
a(0) = 1, a(1) = 2/(1/1 + 1/1) = 1, a(2) = 2/(1/1 + 1/2) = 4/3, a(3) = 2/(1/(4/3) + 1/3) = 24/13, a(4) = 2/(1/(24/13) + 1/4) = 48/19, etc. This sequence gives the numerators: 1, 1, 4, 24, 48, ...
Links
- Eric Weisstein's World of Mathematics, Harmonic Mean.
- Eric Weisstein's World of Mathematics, Lerch Transcendent.
- Wikipedia, Harmonic mean.
Crossrefs
Programs
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Mathematica
Table[1/(1/2^n - Re[LerchPhi[2, 1, n + 1]]), {n, 0, 24}] // Numerator (* or *) a[0] = 1; a[n_Integer] := a[n] = 2/(1/a[n-1] + 1/n); Table[a[n], {n, 0, 24}] // Numerator
Formula
a(n) = numerator(1/(1/2^n - Re(Phi(2, 1, n+1)))), where Phi(z, s, a) is the Lerch transcendent.