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A354506
a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} (-1)^(k/d+1) )/(k * (n-k)!).
3
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
1,2
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.
PROG
(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)))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Aug 15 2022
STATUS
approved