Let a(adsbygoogle = window.adsbygoogle || []).push({}); _{n,m}be defined for the non-negative integers n and m such that n ≥ m.

a_{n,0}= 1

a_{m,m}= m!

a_{n+1,m+1}= (m+1) * a_{n,m}+ a_{n,m+1}

Is there an explicit formula f such that f(n,m) = a_{n,m}?

Here are the first numbers of the sequence:

[itex]

\begin{align}

&m&0&1&2&3&4\\

n\\

0&&1\\

1&&1&1\\

2&&1&3&2\\

3&&1&6&11&6\\

4&&1&10&35&50&24\\

5&&1&5&85&225&274&12\\

\end{align}

[/itex]

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# Any ideas for an explicit formula?

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