[seqfan] Re: A158415

[Maximilian Hasler]

A000992  a(n)= Sum_{k=1 ... floor(n/2)} a(k)a(n-k) with a(1) = 1.
1, 1, 1, 2, 3, 6, 11, 24, 47, 103, 214, 481, 1030, 2337, 5131, 11813,
26329, ...	OFFSET 	1,4

According to the current definition of this sequence, one should have
a(2) = a(1)+a(1) = 2.
unless I overlook something. Even adjusting the offset to 0 would not
correct the problem. I don't understand ...

OTOH I found the values a(n+2) when I calculated the obvious upper
bound b(n) of Vladimir's sequence, viz
b(n+1) = b(n) + sum( i=1..n/2, b(i) b(n-i)) ; b(1)=1

So if things are adjusted such that A000992(n) = b(n+1(?)), one could
add the comment:
"
Also: number of inequivalent expressions that can be formed with n
symbols among {1,f,b}, where 1 is nullary, f is unary, and b is a
function symmetric in its 2 arguments.
"

Maximilian



On Sat, Mar 21, 2009 at 7:27 PM, Vladimir Reshetnikov
<v.reshetnikov at gmail.com> wrote:
> Dear all,
>
> Can anybody suggest an algorithm for calculating the terms of A158415?
>
> Thanks
> Vladimir
>
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