OFFSET
1,2
FORMULA
a(n) = Sum_{k=1..n} A352013(k) * binomial(n,k).
E.g.f.: -exp(x) * Sum_{k>0} (-1)^k * (exp(x^k) - 1)/k.
E.g.f.: exp(x) * Sum_{k>0} log(1+x^k)/k!.
PROG
(PARI) a(n) = n!*sum(k=1, n, sumdiv(k, d, (-1)^(d+1)/(d*(k/d)!))/(n-k)!);
(PARI) a352013(n) = sumdiv(n, d, (-1)^(n/d+1)*(n-1)!/(d-1)!);
a(n) = sum(k=1, n, a352013(k)*binomial(n, k));
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-exp(x)*sum(k=1, N, (-1)^k*(exp(x^k)-1)/k)))
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)*sum(k=1, N, log(1+x^k)/k!)))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Aug 15 2022
STATUS
approved