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

0,3

Links

Table of n, a(n) for n=0..24.

Eric Weisstein's World of Mathematics, Harmonic Mean.

Eric Weisstein's World of Mathematics, Lerch Transcendent.

Wikipedia, Harmonic mean.

Formula

a(n) = numerator(1/(1/2^n - Re(Phi(2, 1, n+1)))), where Phi(z, s, a) is the Lerch transcendent.

Example

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, ...

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

Crossrefs

Cf. A353251 (denominators).

Cf. A003149, A136128, A191778 (has many terms in common), A241519, A242376.

Sequence in context: A090821 A226575 A052645 * A191778 A157625 A128205

Adjacent sequences: A353247 A353248 A353249 * A353251 A353252 A353253

Keyword

nonn,frac

Author

Vladimir Reshetnikov, Apr 08 2022

Status

approved