The sequence of double factorials for even n = 0, 2, 4, 6, 8,... starts as 1, 2, 8, 48, 384, 3840, 46080, 645120,... (sequence A000165 in the OEIS) The sequence of double factorials for odd n = 1, 3, 5, 7, 9,... starts as 1, 3, 15, 105, 945, 10395, 135135,... (sequence A001147 in the OEIS) Meserve (1948) (possibly the earliest publication to use double factorial notation) states that the double factorial was originally introduced in order to simplify the expression of certain trigonometric integrals arising in the derivation of the Wallis product.
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