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

1, 1, 3, 10, 43, 216, 1308, 9157, 73299, 659701, 6597228, 72569509, 870835456, 11320860929, 158492062165, 2377380932700, 38038094996499, 646647614940484, 11639657069589711, 221153484322204510, 4423069686450687468, 92884463415464445994, 2043458195140290381379, 46999538488226678771718

Offset: 1

Author

Ilya Gutkovskiy, Aug 24 2018

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..450

Crossrefs

Cf. A003238, A038046, A197953.

Programs

Maple

f:= proc(n) option remember;
add(d*procname(d),d=numtheory:-divisors(n-1))
end proc:
f(1):= 1:
map(f, [$1..30]); # Robert Israel, Aug 24 2018

Mathematica

a[n_] := a[n] = Sum[d a[d], {d, Divisors[n - 1]}]; a[1] = 1; Table[a[n], {n, 24}]

PARI

a(n) = if (n==1, 1, sumdiv(n-1, d, d*a(d))); \\ Michel Marcus, Aug 25 2018

Formula

L.g.f.: -log(Product_{n>=1} (1 - x^n)^a(n)) = Sum_{n>=1} a(n+1)*x^n/n.

a(n) ~ c * (n-1)!, where c = 1.818022128135673369551657167939033389270758547856526032865616543756614556559... - Vaclav Kotesovec, Aug 25 2018