The last Democratic President to be in office when a recession officially began in the US was Carter.
To contrast - every Republican who was elected to the office since 1900 had at least one recession begin during his tenure with several having 2 (including one whose image is atop Mt Rushmore).
Ford doesn't count since he was appointed VP and subsequently finished Nixon's 2nd term.
There will be at least one recession while Trump reigns - the only question is when it will start.