A173133 a(n) = Sinh[(2n-1) ArcSinh[n]].

0, 1, 38, 4443, 1166876, 546365045, 400680904674, 423859315570607, 611038907405197432, 1151555487914640463209, 2748476184146759127540190, 8102732939160371170806346243, 28915133156938367486730067779348

Offset: 0

Author

Artur Jasinski, Feb 10 2010

Keywords

• nonn

Crossrefs

Cf. A058331, A001079, A037270, A071253, A108741, A132592, A146311, A146312, A146313, A173115, A173116, A173121, A173127, A173128, A173129, A173130, A173131.

Programs

Mathematica

Table[Round[Sinh[(2 n - 1) ArcSinh[n]]], {n, 0, 20}] (* Artur Jasinski *)
Round[Table[1/2 (n - Sqrt[1 + n^2])^(2 n - 1) + 1/2 (n + Sqrt[1 + n^2])^(2 n - 1), {n, 0, 10}]] (* Artur Jasinski, Feb 14 2010 *)

Formula

a(n) = 1/2 (n - sqrt(1 + n^2))^(2 n - 1) + 1/2 (n + sqrt(1 + n^2))^(2 n - 1). - Artur Jasinski, Feb 14 2010

Extensions

Minor edits by Vaclav Kotesovec, Apr 05 2016