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

1,2

Links

Table of n, a(n) for n=1..22.

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).

Prog

(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))))

Crossrefs

Cf. A308345, A356406.

Sequence in context: A149441 A149442 A078468 * A149443 A125656 A279159

Adjacent sequences: A354336 A354337 A354338 * A354340 A354341 A354342

Keyword

nonn

Author

Seiichi Manyama, Aug 15 2022

Status

approved