self ref function and its generating function

Asked Oct 04 '20 at 11:25

Active Oct 04 '20 at 11:25

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Let $h_0 =1 $ and $ h_n = h_{n-1} + \sum \limits_{j=0}^{n-1} h_j h_{n-1-j}$ for $n\geq 1$,

And i am asked to find closed form for $H(x) = \sum h_n x^n$ ?

With a recurrence of finite number of previous terms I now know how to do it, but this is new to me!

Thanks in advance.

asked Oct 04 '20 at 11:25

Ahmad

1

Think about $H(x)^2$. – Angina Seng Oct 04 '20 at 11:27
@AnginaSeng when $a_n= \sum a_{j} a_{n-1-j}$ , does this trick $A(x)^2$ always works ?! – Ahmad Oct 04 '20 at 11:31

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