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Number of connected functions on n points with a single labeled point.
3

%I #10 Jan 03 2021 06:36:18

%S 0,1,3,9,27,81,242,722,2150,6395,19003,56428,167458,496724,1472835,

%T 4365692,12936998,38327764,113529027,336221554,995586119,2947641940,

%U 8726093434,25829729702,76450357119,226257478851,669566448376,1981320898874,5862583555761

%N Number of connected functions on n points with a single labeled point.

%H Alois P. Heinz, <a href="/A038002/b038002.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: B(x)(B(x)+1) where B(x) is g.f. of A000107.

%F a(n) = Sum_{k=1..n} k * A339067(n,k). - _Alois P. Heinz_, Dec 04 2020

%F G.f.: A000081(x) / (1 - A000081(x))^2, where A000081(x) is the g.f. of A000081. - _Vaclav Kotesovec_, Jan 03 2021

%Y Cf. A000107, A027853, A339067.

%K nonn

%O 0,3

%A _Christian G. Bower_