A350135 - OEIS

%I #17 Dec 20 2021 07:34:30

%S 1,1,27,2890,705740,310181886,215071984512,216357598418676,

%T 298018065222408960,538758820820128412790,1237604585414359892787200,

%U 3521561770316172974098259916,12159265179096745219044911480832,50086112147669900240287215353718700,242646275221231775443338250567758643200

%N Number of endofunctions on [2n] whose smallest connected component has size n.

%C a(0) = 1 by convention.

%C Number of endofunctions on [2n] with two connected components of size n.

%H Alois P. Heinz, <a href="/A350135/b350135.txt">Table of n, a(n) for n = 0..193</a>

%F a(n) = A347999(2n,n).

%F a(n) = A001865(n)^2 * A088218(n) for n >= 1.

%e a(1) = 1: 12.

%p a:= n-> `if`(n=0, 1, add(n^(n-j)*(n-1)!/(n-j)!, j=1..n)^2*binomial(2*n, n)/2):

%p seq(a(n), n=0..14);

%Y Cf. A001865, A065456, A088218, A347999.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Dec 15 2021