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f ( x ) = ∑ n = 0 ∞ ( − 1 ) n x n ( n + 2 ) ! 2 ( n ! ) = ∑ n = 0 ∞ ( − 1 ) n x n ( n + 2 ) ( n + 1 ) 2 {\displaystyle f(x)=\sum _{n=0}^{\infty }(-1)^{n}x^{n}{\frac {(n+2)!}{2(n!)}}=\sum _{n=0}^{\infty }(-1)^{n}x^{n}{\frac {(n+2)(n+1)}{2}}\,}