A354508 a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} (-1)^(k/d+1) * d^2 )/(k * (n-k)!).

1, 5, 32, 168, 1189, 8785, 77384, 646296, 7306737, 79997893, 1005481784, 12518370128, 184109233125, 2671256865121, 47934480000112, 754158322407248, 13813898274148737, 262680987222463269, 5518034466415262320, 107988236156057411096, 2605128008760639636677

Offset: 1

Author

Seiichi Manyama, Aug 15 2022

Keywords

• nonn

Crossrefs

Cf. A354506, A354507.

Cf. A078306, A356391.

Programs

PARI

a(n) = n!*sum(k=1, n, sumdiv(k, d, (-1)^(k/d+1)*d^2)/(k*(n-k)!));

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(-exp(x)*sum(k=1, N, (-x)^k/(k*(1-x^k)^2))))

PARI

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

Formula

a(n) = n! * Sum_{k=1..n} A078306(k)/(k * (n-k)!).

E.g.f.: -exp(x) * Sum_{k>0} (-x)^k/(k * (1 - x^k)^2).

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