[seqfan] person needing help with sequences

[N. J. A. Sloane]

Dear Seq Fans, I received a request for
assistance - would anyone like to help him?

There were 2 emails:

Date: Fri, 13 Aug 2010 13:04:54 +0200
Subject: can you help me, please
From: Mohamed Jalel Atia <jalel.atia at gmail.com>

Can you help me with this, please:
I found the following integer sequences and I would like to ask you if meet
them:

1,15,49,6435,1571191,...

0,4,12,1624,390680,...

1,7,25,3187,789831,...

and later

Subject: Re: can you help me, please
From: Mohamed Jalel Atia <jalel.atia at gmail.com>
To: njas at research.att.com

Dear Prof. Sloane,
These sequences come from the recurrence coefficients of a polynomial
sequence P_n Orthogonal  on [-1,1] with respect to the weight function
w(x)=\abs(x-1/2)/\sqrt (1-x)+ \abs(x+1/2)/\sqrt (1+x),
P_n fulfill
P_0=1, P_1=x,
P_{n+2}=xP_{n+1}-\gamma_{n+1}P_n, n\geq 0,
whrer
\gamma_1=1/2
\gamma_2=1/4
\gamma_3=7/30
\gamma_4=4/15
\gamma_5=1/4
\gamma_6=12/49
\gamma_7=25/98
\gamma_8=1/4
\gamma_9=3187/12870
\gamma_10=1624/6435
\gamma_11=1/4
\gamma_12=390680/1571191

in such a way that

\gamma_3+\gamma_4=1/2
\gamma_6+\gamma_7=1/2
\gamma_9+\gamma_10=1/2
etc....

Thank you very much,
Mohamed Jalel Atia.

Neil