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We prove a recent conjecture, due to Vigren and Dieckmann, about an explicittriple sum formula for a series from Ramanujan's Notebooks. We shall give twoproofs: the first one is by evaluation and based on the identity\begin{equation*}  \sum_{k=0}^\infty \frac{(x+k)^{m+k}}{k!}e^{-u(x+k)} u^k  = \sum_{j=0}^\infty \sum_{i=0}^{m}\binom{m+j}{i}  \stirl{m+j-i}{j}x^iu^j, \end{equation*} where $\genfrac\{\}{0pt}{}{n}{k}$ isa Stirling number of the second kind, and the second one is combinatorial innature and by induction.

Proof of an explicit formula for a series from Ramanujan's Notebooks via tree functions