A260122 a(n) = floor( Product_{k = 1..n} k^(k/2) ).

1, 2, 10, 166, 9295, 2007754, 1822022612, 7463004618900, 146894319913813741, 14689431991381374106820, 7846297508164921345697431897, 23428918818620324499511000487089219, 407740674993626332726840969430118771134776

Offset: 1

Author

Ilya Gutkovskiy, Jul 17 2015

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..50
• Eric Weisstein's World of Mathematics, Hyperfactorial

Crossrefs

Cf. A002109, A074962.

Programs

Mathematica

Table[Floor[Sqrt[Hyperfactorial[n]]], {n, 1, 12}]

PARI

a(n) = sqrtint(prod(k=2,n,k^k)) \\ Charles R Greathouse IV, Jul 17 2015

Formula

a(n) = floor(sqrt(A002109(n))) = A000196(A002109(n)).

a(n) ~ sqrt(A)*n^(n*(n+1)/4+1/24)/exp(n^2/8), where A is the Glaisher-Kinkelin constant (A074962). - Ilya Gutkovskiy, Dec 27 2016