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

%I A350157 #24 Apr 27 2022 08:50:55
%S A350157 0,1,7,61,709,9911,167111,3237921,71850913,1780353439,49100614399,
%T A350157 1482061739423,48873720208853,1740252983702871,66793644836081827,
%U A350157 2740470162691675711,120029057782404141841,5575505641199441262767,274412698693082818767335,14236421024010426118259883
%N A350157 Total number of nodes in the smallest connected component summed over all endofunctions on [n].
%H A350157 Alois P. Heinz, <a href="/A350157/b350157.txt">Table of n, a(n) for n = 0..385</a>
%F A350157 a(n) = Sum_{k=1..n} k * A347999(n,k).
%e A350157 a(2) = 7 = 2 + 2 + 1 + 2: 11, 22, 12, 21.
%p A350157 g:= proc(n) option remember; add(n^(n-j)*(n-1)!/(n-j)!, j=1..n) end:
%p A350157 b:= proc(n, m) option remember; `if`(n=0, x^m, add(
%p A350157       b(n-i, min(m, i))*g(i)*binomial(n-1, i-1), i=1..n))
%p A350157     end:
%p A350157 a:= n-> (p-> add(coeff(p, x, i)*i, i=0..n))(b(n,n)):
%p A350157 seq(a(n), n=0..23);
%t A350157 g[n_] := g[n] = Sum[n^(n - j)*(n - 1)!/(n - j)!, {j, 1, n}];
%t A350157 b[n_, m_] := b[n, m] = If[n == 0, x^m, Sum[
%t A350157      b[n - i, Min[m, i]]*g[i]*Binomial[n - 1, i - 1], {i, 1, n}]];
%t A350157 a[n_] := Function[p, Sum[Coefficient[p, x, i]*i, {i, 0, n}]][b[n, n]];
%t A350157 Table[a[n], {n, 0, 23}] (* _Jean-François Alcover_, Apr 27 2022, after _Alois P. Heinz_ *)
%Y A350157 Column k=1 of A350202.
%Y A350157 Cf. A000312, A001865, A007778, A209327, A347999.
%K A350157 nonn
%O A350157 0,3
%A A350157 _Alois P. Heinz_, Dec 17 2021