A350157 Total number of nodes in the smallest connected component summed over all endofunctions on [n].

0, 1, 7, 61, 709, 9911, 167111, 3237921, 71850913, 1780353439, 49100614399, 1482061739423, 48873720208853, 1740252983702871, 66793644836081827, 2740470162691675711, 120029057782404141841, 5575505641199441262767, 274412698693082818767335, 14236421024010426118259883

Offset: 0

Author

Alois P. Heinz, Dec 17 2021

Keywords

• nonn

Examples

			a(2) = 7 = 2 + 2 + 1 + 2: 11, 22, 12, 21.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..385

Crossrefs

Column k=1 of A350202.

Cf. A000312, A001865, A007778, A209327, A347999.

Programs

Maple

g:= proc(n) option remember; add(n^(n-j)*(n-1)!/(n-j)!, j=1..n) end:
b:= proc(n, m) option remember; `if`(n=0, x^m, add(
      b(n-i, min(m, i))*g(i)*binomial(n-1, i-1), i=1..n))
    end:
a:= n-> (p-> add(coeff(p, x, i)*i, i=0..n))(b(n,n)):
seq(a(n), n=0..23);

Mathematica

g[n_] := g[n] = Sum[n^(n - j)*(n - 1)!/(n - j)!, {j, 1, n}];
b[n_, m_] := b[n, m] = If[n == 0, x^m, Sum[
     b[n - i, Min[m, i]]*g[i]*Binomial[n - 1, i - 1], {i, 1, n}]];
a[n_] := Function[p, Sum[Coefficient[p, x, i]*i, {i, 0, n}]][b[n, n]];
Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Apr 27 2022, after Alois P. Heinz *)

Formula

a(n) = Sum_{k=1..n} k * A347999(n,k).