A354340 a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} d^(k/d + 1) )/(k * (n-k)!).

1, 7, 38, 264, 1629, 16075, 122366, 1414952, 16076913, 213998983, 2112313774, 53581378400, 664573162941, 9967808211387, 239545427723062, 5933102008956848, 79857813309308609, 2677379355344673255, 44453311791217697686, 1743982053518367438616

Offset: 1

Author

Seiichi Manyama, Aug 15 2022

Keywords

• nonn

Crossrefs

Cf. A078308, A353992, A354848, A356598.

Programs

PARI

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

PARI

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

Formula

a(n) = n! * Sum_{k=1..n} A078308(k)/(k * (n-k)!).

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