After researching what could cause an instant kernel panic with no documentation or messages in kdump, I found that if manually execute the following code (warning: will cause system disruption, I am not held responsible for your copy and pasting):

echo c > /proc/sysrq-trigger

More information regarding this can be found on the Old Internet Archives at https://web.archive.org/web/20160816230132/https://www.kernel.org/doc/Documentation/sysrq.txt