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A316073 a(n) is the n-th term of the inverse Weigh transform of j-> n^(j-1).

%I A316073 #12 Dec 30 2020 04:34:38
%S A316073 1,2,6,46,420,5185,77658,1376768,28133616,651325653,16846515510,
%T A316073 481472773386,15067838554860,512473605894549,18821719654854998,
%U A316073 742395982483047976,31299550394528466960,1404629090183809673484,66851805805525048040334,3363381327122907537090234
%N A316073 a(n) is the n-th term of the inverse Weigh transform of j-> n^(j-1).
%H A316073 Alois P. Heinz, <a href="/A316073/b316073.txt">Table of n, a(n) for n = 1..200</a>
%F A316073 a(n) ~ (1 - exp(-1)) * n^(n-1). - _Vaclav Kotesovec_, Oct 08 2019
%p A316073 b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A316073       add(binomial(g(i, k), j)*b(n-i*j, i-1,k), j=0..n/i)))
%p A316073     end:
%p A316073 g:= proc(n, k) option remember; k^(n-1)-b(n, n-1, k) end:
%p A316073 a:= n-> g(n$2):
%p A316073 seq(a(n), n=1..21);
%t A316073 b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0,
%t A316073     Sum[Binomial[g[i, k], j] b[n - i j, i - 1, k], {j, 0, n/i}]]];
%t A316073 g[n_, k_] := g[n, k] = k^(n - 1) - b[n, n - 1, k];
%t A316073 a[n_] := g[n, n];
%t A316073 Array[a, 21] (* _Jean-François Alcover_, Dec 29 2020, after _Alois P. Heinz_ *)
%Y A316073 Cf. A306173.
%K A316073 nonn
%O A316073 1,2
%A A316073 _Alois P. Heinz_, Jun 23 2018