A350135 Number of endofunctions on [2n] whose smallest connected component has size n.

1, 1, 27, 2890, 705740, 310181886, 215071984512, 216357598418676, 298018065222408960, 538758820820128412790, 1237604585414359892787200, 3521561770316172974098259916, 12159265179096745219044911480832, 50086112147669900240287215353718700, 242646275221231775443338250567758643200

Offset

0,3

Comments

a(0) = 1 by convention.

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

Links

Alois P. Heinz, Table of n, a(n) for n = 0..193

Formula

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

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

Example

a(1) = 1: 12.

Maple

a:= n-> `if`(n=0, 1, add(n^(n-j)*(n-1)!/(n-j)!, j=1..n)^2*binomial(2*n, n)/2):
seq(a(n), n=0..14);

Crossrefs

Cf. A001865, A065456, A088218, A347999.

Sequence in context: A048567 A227492 A027363 * A085529 A132659 A104131

Adjacent sequences: A350132 A350133 A350134 * A350136 A350137 A350138

Keyword

nonn

Author

Alois P. Heinz, Dec 15 2021

Status

approved