%I #11 Jul 31 2024 09:09:15
%S 1,1,4,28,278,3554,55382,1015750,21401830,508932130,13475090126,
%T 393026736854,12518884854734,432357148756210,16092438499462630,
%U 642170913160160710,27351173629037613494,1238472705706192189442,59411223892666111129022,3010044856761072109710262
%N Defined by: Sum_{i=1..n} i*a(i)/n^i = 1, n>=1.
%H Seiichi Manyama, <a href="/A374601/b374601.txt">Table of n, a(n) for n = 1..387</a>
%F a(n) = n^(n-1) - Sum_{i=1..n-1} n^(n-1-i)*i*a(i))
%F a(n) = A374562(n)/n.
%e 1*a(1)/1^1 = 1, so a(1) = 1.
%e 1*a(1)/2^1 + 2*a(2)/2^2 = 1, so a(2) = 1.
%e 1*a(1)/3^1 + 2*a(2)/3^2 + 3*a(3)/3^3 = 1, so a(3)=4.
%p a:= proc(n) option remember; `if`(n<1, 0,
%p n^(n-1)-add(n^(n-1-i)*a(i)*i, i=1..n-1))
%p end:
%p seq(a(n), n=1..20); # _Alois P. Heinz_, Jul 13 2024
%t a[n_]:=a[n]=n^(n-1)-Sum[n^(n-1-i)*i*a[i],{i,1,n-1}]
%o (PARI) a(n)=n^(n-1)-sum(i=1,n-1,n^(n-1-i)*i*a(i))
%Y Cf. A374562.
%K nonn
%O 1,3
%A _Luc Rousseau_, Jul 13 2024