We prove a recent conjecture, due to Vigren and Dieckmann, about an explicit triple sum formula for a series from Ramanujan's Notebooks. We shall give two proofs: 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 $\genfrac\{ \}{ 0pt}{ }{ n}{ k}$ is a Stirling number of the second kind, and the second one is combinatorial in nature and by induction.
Categories: math.CO