There are two separate and independent aspects in play: (a) the size of the operator symbols (\sum, \prod, \int, etc) and (b) the placement of the upper and lower limits. In the case of \sum, what you've (re-)discovered is that if \displaystyle is in use, LaTeX (and many other typesetting systems too…) is to combine a large symbol size with placing the limits of summation above and below rather than to the side of the symbol. To override the default for the placement of the limits (but not for the size of the symbol), it's necessary to insert the directive \nolimitsafter\sum.
– MicoFeb 07 '20 at 09:18
\sum_{j=1}^k S(n,j)to\sum\nolimits_{j=1}^k S(n,j). – Mico Feb 07 '20 at 06:54displayvsinline. – J. Doe Feb 07 '20 at 09:09\sum,\prod,\int, etc) and (b) the placement of the upper and lower limits. In the case of\sum, what you've (re-)discovered is that if\displaystyleis in use, LaTeX (and many other typesetting systems too…) is to combine a large symbol size with placing the limits of summation above and below rather than to the side of the symbol. To override the default for the placement of the limits (but not for the size of the symbol), it's necessary to insert the directive\nolimitsafter\sum. – Mico Feb 07 '20 at 09:18