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2.2: Permutaciones de posición prohibida
https://espanol.libretexts.org/Matematicas/Combinatoria_y_Matematicas_Discretas/Combinatoria_y_Teor%C3%ADa_Gr%C3%A1fica_(Guichard)/02%3A_Inclusi%C3%B3n-Exclusi%C3%B3n/2.02%3A_Permutaciones_de_posici%C3%B3n_prohibida
\[\eqalignno{ D_n&=nD_{n-1}-D_{n-1}+(n-1)D_{n-2}&(*)\cr &=nD_{n-1}-(n-2)(D_{n-2}+D_{n-3})+(n-1)D_{n-2}\cr &=nD_{n-1}-(n-2)D_{n-2}-(n-2)D_{n-3}+(n-1)D_{n-2}\cr &=nD_{n-1}+D_{n-2}-(n-2)D_{n-3}&(*)\cr &=... $\eqalignno{ D_n&=nD_{n-1}-D_{n-1}+(n-1)D_{n-2}&(*)\cr &=nD_{n-1}-(n-2)(D_{n-2}+D_{n-3})+(n-1)D_{n-2}\cr &=nD_{n-1}-(n-2)D_{n-2}-(n-2)D_{n-3}+(n-1)D_{n-2}\cr &=nD_{n-1}+D_{n-2}-(n-2)D_{n-3}&(*)\cr &=nD_{n-1}+(n-3)(D_{n-3}+D_{n-4})-(n-2)D_{n-3}\cr &=nD_{n-1}+(n-3)D_{n-3}+(n-3)D_{n-4}-(n-2)D_{n-3}\cr &=nD_{n-1}-D_{n-3}+(n-3)D_{n-4}&(*)\cr &=nD_{n-1}-(n-4)(D_{n-4}+D_{n-5})+(n-3)D_{n-4}\cr &=nD_{n-1}-(n-4)D_{n-4}-(n-4)D_{n-5}+(n-3)D_{n-4}\cr &=nD_{n-1}+D_{n-4}-(n-4)D_{n-5}.&(*)\cr }\nonumber$

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