A nice little curio.
1 = 1!
2(3) = 6 = 3!
4(5)(6) = 120 = 5!
7(8)(9)(10) = 5040 = 7!
Are there any other examples of products of 'some' consecutive integers equalling factorials? Is there a proof that there is not? To be clear I am asking if the pattern above continues for all the triangular numbers (in bold)? It does not appear to hold for the next few examples so I conjecture that the pattern only holds for the triangular numbers above. Is this conjecture known or proven/disproven?