A128406 a(n) = (n+1)*2^(n*(n+1)).

1, 8, 192, 16384, 5242880, 6442450944, 30786325577728, 576460752303423488, 42501298345826806923264, 12379400392853802748991242240, 14278816360970775978458864905355264, 65334214448820184984967924626899496599552, 1187470080331358621040493926581979953470445191168

Offset: 0

Author

Paul Barry, Mar 01 2007

Keywords

• easy
• nonn

Comments

Hankel transform of A069723.

With offset 1, a(n) is the number of vertices with in-degree = 0 over all labeled digraphs (with self loops allowed) on n vertices. Equivalently, the number of elements in all labeled relations on an n-set that have no preimage. - Geoffrey Critzer, Aug 16 2016

Crossrefs

Cf. A006125, A069723, A095340.

Programs

Mathematica

Table[n 2^(n - 1) 2^(n - 1)^2, {n, 1, 10}]
Table[(n+1)2^(n(n+1)),{n,0,20}] (* Harvey P. Dale, Jun 21 2021 *)

Formula

a(n) = A095340(n)*A006125(n+1).