A354339 a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} 1/(d * (k/d)^d) )/(n-k)!.

1, 4, 13, 47, 188, 939, 5332, 36196, 279085, 2464592, 23591753, 259110191, 3030440580, 38874240339, 535736880460, 8027897509136, 126034992483809, 2144006461602308, 38072688073456557, 723023026186433271, 14342481336066795732, 301141522554921194275

Offset: 1

Author

Seiichi Manyama, Aug 15 2022

Keywords

• nonn

Crossrefs

Cf. A308345, A356406.

Programs

PARI

a308345(n) = n!*sumdiv(n, d, 1/(d*(n/d)^d));
a(n) = sum(k=1, n, a308345(k)*binomial(n, k));

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(-exp(x)*sum(k=1, N, log(1-x^k/k))))

Formula

a(n) = Sum_{k=1..n} A308345(k) * binomial(n,k).

E.g.f.: -exp(x) * Sum_{k>0} log(1-x^k/k).