login
A354338
a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} 1/(d * (k/d)!) )/(n-k)!.
1
1, 4, 12, 41, 145, 742, 3962, 27659, 215131, 1996356, 17300360, 218809109, 2421142269, 31105286682, 427776526574, 6964677268087, 97708052695959, 1856379196278120, 30362097934331500, 606395795174882161, 12016899266310773097, 261771941015999635310
OFFSET
1,2
FORMULA
a(n) = Sum_{k=1..n} A087906(k) * binomial(n,k).
E.g.f.: exp(x) * Sum_{k>0} (exp(x^k) - 1)/k.
E.g.f.: -exp(x) * Sum_{k>0} log(1-x^k)/k!.
PROG
(PARI) a087906(n) = n!*sumdiv(n, d, 1/(d*(n/d)!));
a(n) = sum(k=1, n, a087906(k)*binomial(n, k));
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)*sum(k=1, N, (exp(x^k)-1)/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
nonn
AUTHOR
Seiichi Manyama, Aug 15 2022
STATUS
approved