A354506 a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} (-1)^(k/d+1) )/(k * (n-k)!).

1, 2, 7, 14, 63, 284, 2385, 3940, 87717, 940126, 12743267, 30055618, 562302323, 9005878920, 423435780989, 2080544097000, 24457758561001, 444510436079706, 17533073308723423, 46973556239255702, 7501223613055891783, 178483805340054632084, 4396051786608296882889, -31788150263554644516724

Offset: 1

Author

Seiichi Manyama, Aug 15 2022

Keywords

• sign

Crossrefs

Cf. A354507, A354508.

Cf. A048272, A356389.

Programs

PARI

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

Formula

a(n) = n! * Sum_{k=1..n} A048272(k)/(k * (n-k)!).

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