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A318372 a(1) = 1; a(n+1) = Sum_{d|n} d*a(d).

%I A318372 #16 May 09 2019 16:11:25
%S A318372 1,1,3,10,43,216,1308,9157,73299,659701,6597228,72569509,870835456,
%T A318372 11320860929,158492062165,2377380932700,38038094996499,
%U A318372 646647614940484,11639657069589711,221153484322204510,4423069686450687468,92884463415464445994,2043458195140290381379,46999538488226678771718
%N A318372 a(1) = 1; a(n+1) = Sum_{d|n} d*a(d).
%H A318372 Seiichi Manyama, <a href="/A318372/b318372.txt">Table of n, a(n) for n = 1..450</a>
%F A318372 L.g.f.: -log(Product_{n>=1} (1 - x^n)^a(n)) = Sum_{n>=1} a(n+1)*x^n/n.
%F A318372 a(n) ~ c * (n-1)!, where c = 1.818022128135673369551657167939033389270758547856526032865616543756614556559... - _Vaclav Kotesovec_, Aug 25 2018
%p A318372 f:= proc(n) option remember;
%p A318372 add(d*procname(d),d=numtheory:-divisors(n-1))
%p A318372 end proc:
%p A318372 f(1):= 1:
%p A318372 map(f, [$1..30]); # _Robert Israel_, Aug 24 2018
%t A318372 a[n_] := a[n] = Sum[d a[d], {d, Divisors[n - 1]}]; a[1] = 1; Table[a[n], {n, 24}]
%o A318372 (PARI) a(n) = if (n==1, 1, sumdiv(n-1, d, d*a(d))); \\ _Michel Marcus_, Aug 25 2018
%Y A318372 Cf. A003238, A038046, A197953.
%K A318372 nonn
%O A318372 1,3
%A A318372 _Ilya Gutkovskiy_, Aug 24 2018