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Recurrence Relationship Help Request

I have been playing with the recurrence relation

\[ p_n = np_{n-1} + p_{n-2} \] such that \( p_0 = 0 , p_1 = 1 \).

I have found a few interesting difference forms for it but no closed form formula. Can anyone find a nice closed form formula, generating function or interpretation for what this might count.

All thoughts appreciated and welcome :)

Note by Roberto Nicolaides
4 months, 2 weeks ago

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Whenever you're investigating a sequence, it's not a bad idea to check the OEIS. This is entry A001053. There doesn't seem to be too much information. Jon Haussmann · 4 months, 2 weeks ago

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@Jon Haussmann Thanks Jon, this is a nice idea :) I did have a quick look and agreed that there was not a lot of info! I will be having a look at bessel funtions soon to try get more intuition on the problem :) Roberto Nicolaides · 4 months, 2 weeks ago

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