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A374601 Defined by: Sum_{i=1..n} i*a(i)/n^i = 1, n>=1.

%I A374601 #16 Mar 30 2025 04:25:50
%S A374601 1,1,4,28,278,3554,55382,1015750,21401830,508932130,13475090126,
%T A374601 393026736854,12518884854734,432357148756210,16092438499462630,
%U A374601 642170913160160710,27351173629037613494,1238472705706192189442,59411223892666111129022,3010044856761072109710262
%N A374601 Defined by: Sum_{i=1..n} i*a(i)/n^i = 1, n>=1.
%H A374601 Seiichi Manyama, <a href="/A374601/b374601.txt">Table of n, a(n) for n = 1..387</a>
%F A374601 a(n) = n^(n-1) - Sum_{i=1..n-1} n^(n-1-i)*i*a(i).
%F A374601 a(n) = A374562(n)/n.
%e A374601 1*a(1)/1^1 = 1, so a(1) = 1.
%e A374601 1*a(1)/2^1 + 2*a(2)/2^2 = 1, so a(2) = 1.
%e A374601 1*a(1)/3^1 + 2*a(2)/3^2 + 3*a(3)/3^3 = 1, so a(3) = 4.
%p A374601 a:= proc(n) option remember; `if`(n<1, 0,
%p A374601       n^(n-1)-add(n^(n-1-i)*a(i)*i, i=1..n-1))
%p A374601     end:
%p A374601 seq(a(n), n=1..20);  # _Alois P. Heinz_, Jul 13 2024
%t A374601 a[n_]:=a[n]=n^(n-1)-Sum[n^(n-1-i)*i*a[i],{i,1,n-1}]
%o A374601 (PARI) a(n)=n^(n-1)-sum(i=1,n-1,n^(n-1-i)*i*a(i))
%Y A374601 Cf. A374562.
%K A374601 nonn
%O A374601 1,3
%A A374601 _Luc Rousseau_, Jul 13 2024