# [seqfan] Re: Zeros in A172390 and A172391

Paul D Hanna pauldhanna at juno.com
Mon Mar 29 14:34:32 CEST 2010

```Joerg (and SeqFans),
Here is a related observation.

Take the convolution square-root of A172390, which proceeds:
[1, 4, 4, -16, -28, 176, 336, -2496, -4956, 40112, 81488, -694720,...]

and compare that to A158100:
[1,4,4,0,4,0,-16,0,-28,0,176,0,336,0,-2496,0,-4956,0,40112,0,81488,...],
for which the g.f. satisfies: A(x) = 1/AGM(1, 1 - 8*x/A(x) ).

So if we remove the odd-indexed terms [4,0,0,0,...] from A158100 we obtain A172390^(1/2).
And the AGM appears in both g.f.s.

Paul

---------- Original Message ----------
From: Joerg Arndt <arndt at jjj.de>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Subject: [seqfan] Re: Zeros in A172390 and A172391
Date: Mon, 29 Mar 2010 07:38:26 +0200

* Joerg Arndt <arndt at jjj.de> [Mar 23. 2010 06:52]:
> [...]
>
> Interesting.  I don't think this is known.
>
It appears that if the 'odd' term 8*x, i.e.
A172390  1, 8, 24, 0, -168, 0, 2112, 0, -32040, 0, 536256, ...
^
this one

is removed then the series is a 4th power of
another one that has all integer coefficients.
Whether this is just another way of putting
the conjecture in question I do not know.
>
> [...]

```