A308345 - OEIS

%I #10 Aug 05 2022 15:36:50

%S 1,2,4,15,48,310,1440,11970,85120,821016,7257600,91707000,958003200,

%T 13440913200,178919989248,2809456650000,41845579776000,

%U 763629026160000,12804747411456000,257140635922025856,4918792391884800000,106876408948152480000

%N Expansion of e.g.f. Sum_{k>=1} log(1/(1 - x^k/k)).

%H Seiichi Manyama, <a href="/A308345/b308345.txt">Table of n, a(n) for n = 1..450</a>

%F a(n) = n! * Sum_{d|n} 1/(d*(n/d)^d).

%F a(n) = A007841(n) - (1/n) * Sum_{k=1..n-1} k*binomial(n,k)*A007841(n-k)*a(k).

%F a(n) ~ 2 * (n-1)!. - _Vaclav Kotesovec_, Feb 16 2020

%t nmax = 22; CoefficientList[Series[Sum[Log[1/(1 - x^k/k)], {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest

%t Table[n! Sum[1/(d (n/d)^d), {d, Divisors[n]}], {n, 1, 22}]

%Y Cf. A007841, A038048, A182926, A182927, A308337.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, May 21 2019