[seqfan] Re: g.f. for a(n)= a(n-1)*2^n+n, a(0)=1 ?

[Max Alekseyev]

Here is an explicit formula for a(n):

a(n) = 2^(n*(n+1)/2) + \sum_{k=1}^n 2^( (n+k+1)*(n-k)/2 ) * k

Max

On Sun, Sep 5, 2010 at 9:31 AM, Georgi Guninski <guninski at guninski.com> wrote:
> i tried to submit:
> a(n)= a(n-1)*2^n+n, a(0)=1
>
> it satisfies both:
> a(n+1) = (2^(n + 1) + 1)*a(n) - 2^n*a(n - 1) + 1
>
> a(n+1) = ((a(n - 2) + 4*a(n - 1) + 4)*a(n) - 2*a(n - 1)^2 - 4*a(n)^2 +
> a(n - 2) - 4*a(n - 1))/(a(n - 2) - 2*a(n - 1))
>
> and is kind of related to:
> A010842 a(n) = n*a(n-1)+2^n
>
> superseeker fails to find g.f., does anyone know one ?
>
>
>
>
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