[seqfan] Possible closed form for A122835

[Vladimir Reshetnikov]

Dear seqfans,

Playing with some integer sequences I accidentally found a formula
which seems to be a closed form (nonrecursive) for A122835. It is only
a guess based only on numerical evidence, I do not have any proof of
it.

a[k_]:=(-4 + 3*2^k*(LerchPhi[1/4, -k, 1/2] + 2*PolyLog[-k, 1/4]))/8

I would be glad if anyone finds a proof (or disproof) of that.

--
Thanks
Vladimir Reshetnikov