A240993 A000142 (n+1) * A002109(n), a product of factorials and hyperfactorials.

1, 2, 24, 2592, 3317760, 62208000000, 20316635136000000, 133852981198454784000000, 20211123400293732996612096000000, 78302033109811407811828935756349440000000, 8613223642079254859301182933198438400000000000000000

Offset: 0

Author

Reinhard Zumkeller, Aug 31 2014

Keywords

• nonn

Comments

a(n+1) / a(n) = A055897(n+2);

row products of the triangle A245334.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..36

Crossrefs

Cf. A000142, A002109, A245334, A055897, A245334, A111063, A074962.

Programs

Haskell

a240993 n = a000142 (n + 1) * a002109 n

Mathematica

Table[(n+1)!*Hyperfactorial[n], {n, 0, 10}] (* Vaclav Kotesovec, Nov 14 2014 *)
Table[(n+1)*(n!)^(n+1)/BarnesG[n+1], {n, 0, 10}] (* Vaclav Kotesovec, Nov 14 2014 *)

Formula

a(n) ~ A * sqrt(2*Pi) * n^(n^2/2+3*n/2+19/12) / exp(n*(n+4)/4), where A = 1.2824271291... is the Glaisher-Kinkelin constant (see A074962). - Vaclav Kotesovec, Nov 14 2014