login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A318372
a(1) = 1; a(n+1) = Sum_{d|n} d*a(d).
4
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
1,3
LINKS
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
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}]
PROG
(PARI) a(n) = if (n==1, 1, sumdiv(n-1, d, d*a(d))); \\ Michel Marcus, Aug 25 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 24 2018
STATUS
approved