[seqfan] Re: Need small amount of help with Apery-like numbers

[Hugo Pfoertner]

Neil, SeqFans,

Table 1 corresponds to the following sequences

# A000172
# bAP2_A.txt a=7 b=2 c=-8
2,10,56,346,2252,15184,104960,739162,5280932,38165260,

# A005258
# bAP2_D.txt a=11 b=3 c=-1
3,19,147,1251,11253,104959,1004307,9793891,96918753,970336269,

# A002893
# bAP2_C.txt a=10 b=3 c=9
3,15,93,639,4653,35169,272835,2157759,17319837,140668065,

# A081085
# bAP2_E.txt a=12 b=4 c=32
4,20,112,676,4304,28496,194240,1353508,9593104,68906320,

# A006077
# bAP2_B.txt a=9 b=3 c=27
3,9,21,9,-297,-2421,-12933,-52407,-145293,-35091,

# A093388
# bAP2_F.txt a=17 b=6 c=72
6,42,312,2394,18756,149136,1199232,9729882,79527084,654089292,

I'll now proceeding to Table 2

Regards

Hugo Pfoertner


On Sun, Aug 6, 2017 at 7:06 PM, Neil Sloane <njasloane at gmail.com> wrote:

> Dear Seq Fans, Here is a small job that I could use help
> with - won't take long, is interesting, and may lead to new sequences
>
> If someone can help, please send me email and post a note here. (But
> please be sure to actually do the job, in the past people have said
> they would help but it never happened. I won't mention any names...)
>
> The Apery numbers are A005259.  There are also 12 "Apery-like
> sequences" which are listed in Tables 1 and 2 of the paper
>
> Amita Malik and Armin Straub, Divisibility properties of sporadic
> Apéry-like numbers, Research in Number Theory, 2016, 2:5;
> https://doi.org/10.1007/s40993-016-0036-8
> URL for free download is
> https://resnumtheor.springeropen.com/articles/10.1007/s40993-016-0036-8
>
> They give formulas for these 12 sequences, but they don't give the
> A-numbers or the initial terms.  In fact they don't mention the OEIS
> at all.
>
> The job is to
> - work out the 12 sequences and make a list of the 12 A-numbers
> - add any missing ones to the OEIS
> - Make a line that says:
> "The 12 Apery-like sequences are A******, ******, ... "
> and add this line to the cross-references section of the 12 sequences
> and also to A005229
> - add a reference to the Malik-Straub paper to the same 12 sequences.
>
> Thanks!
>
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