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The "2nd factorial" is defined as \(n§ = \prod^{n}_{i = 1} i^i^2 = 1^1^2 \cdot 2^2^2 \cdot 3^3^2 \cdot 4^4^2 \cdot \ldots \cdot n^n^2\).[1]

The first few values of \(n§\) for \(n = 1, 2, 3, 4, \ldots\) are 1, 16, 314,928, 1,352,605,460,594,688, 403,107,840,000,000,000,000,000,000,000,000, 4,157,825,501,361,955,044,460,594,652,554,199,040,000,000,000,000,000,000,000,000, ... (OEIS A051675). The sum of the reciprocals of these numbers is 2.2592954398150629....

Sources Edit

  1. Hyperfactorial from Wolfram MathWorld
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