[seqfan] Re: Asymptotic behaviour of A034824 and friends

[Rob Arthan]

I wrote:

> I would like to estimate how many trees there are with height at most 8 and with at most 2^64 nodes.
> I.e., I want to estimate the sum of the first 2^64 terms of A034824. Does anyone know the
> asymptotic behaviour of this sequence? Or even better, the general case for height at most H
> and at most N nodes, with H fixed and with N tending to infinity? 
> Are you looking for A000081 = row sums of A034781? If so, then A000081 has
> an asymptotic formula for the n-th term from the Knuth/Polya reference
> there. Also a recurrence formula is given without proof or a source.
> 
> http://oeis.org/A000081
> 
> http://oeis.org/A034781
> 
> Ed Jeffery
> 
No, I was looking for the row sums of A034781 truncated after the 8th column. That is A034825 (not A034824
as I mistakenly said).

Regards,

Rob.