Hard Series

What is the next number in this series?

4,12,84,3612....




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A girl has as many brothers as sisters, but each brother has only half as many brothers as sisters. How many brothers and sisters are there in the family?

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What came first, the chicken or the egg?

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John went to a parrot shop in Mexico, and the parrot owner told him that his parrot is so unique that he repeats everything he hears. John got excited and immediately bought the parrot. John went home and spoke many words, but the parrot does not repeat anything.
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There is a cryptic organization called Cicada 3301 that posts challenging puzzles online, possibly to recruit codebreakers and linguists.