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a(n) = (n+1)*2^(n*(n+1)).
0

%I #13 Jun 21 2021 16:27:42

%S 1,8,192,16384,5242880,6442450944,30786325577728,576460752303423488,

%T 42501298345826806923264,12379400392853802748991242240,

%U 14278816360970775978458864905355264,65334214448820184984967924626899496599552,1187470080331358621040493926581979953470445191168

%N a(n) = (n+1)*2^(n*(n+1)).

%C Hankel transform of A069723.

%C 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

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

%t Table[n 2^(n - 1) 2^(n - 1)^2, {n, 1, 10}]

%t Table[(n+1)2^(n(n+1)),{n,0,20}] (* _Harvey P. Dale_, Jun 21 2021 *)

%Y Cf. A006125, A069723, A095340.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Mar 01 2007