# Dobiإ„ski’s formula

A derivation of Dobiإ„ski’s formula is reproduced below. Why does the upper limit on the first sum change from nn to ∞\infty ? (See the red-boxed portion.)

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have you seen the change of integration for a double integral? I assume he permuted the order to take advantage of the close form of the inner summation.
– Chinny84
Oct 20 at 19:50

1

Exactly, +∞∑k=1k∑j=0\sum_{k=1}^{+\infty}\sum_{j=0}^{k} is turned into +∞∑j=0∑k≥j\sum_{j=0}^{+\infty}\sum_{k\geq j}
– Jack D’Aurizio
Oct 20 at 20:32

In such a question, you should recall that B(n)B(n) is the nnth Bell number with a reference to a definition/explanation such as can be found in (en.wikipedia.org/wiki/Dobiإ„ski’s_formula). It is important that a text is self-contained.
– JeanMarie
Oct 20 at 21:24

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