[seqfan] Re: Connection between A2450 and A321873?

[neil greubel]

Yes. The series for A002450 is 3*Sum_{n=1..infty} 1/(4^n -1) which can be
represented as 3*Sum_{n=1..infty} (1/4)^n/(1 - (1/4)^n) = 3*L(1/4), where
L(x) is the Lambert series. The QPolyGamma formula is the Mathematica
notation for the Lambert series.

On Wed, Oct 23, 2019 at 12:30 AM Alonso Del Arte <alonso.delarte at gmail.com>
wrote:

> One of the comments in A002450 states that
>
> > Sum_{n >= 1} 1/a(n) converges to (3*(log[4/3] - QPolyGamma[0, 1,
> 1/4]))/log[4] = 1.263293...
>
> Is this number the constant in A321873?
>
> Al
>
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