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A356667
Expansion of e.g.f. Sum_{k>=0} x^k / (1 - k*x^k/k!).
1
1, 1, 4, 12, 72, 240, 2520, 10080, 127680, 816480, 11037600, 79833600, 1514177280, 12454041600, 261655954560, 2699348652000, 62869385779200, 711374856192000, 19407798693803520, 243290200817664000, 7300765959334848000, 102980278869910041600
OFFSET
0,3
FORMULA
a(n) = n! * Sum_{d|n} 1/((d-1)!^(n/d-1)) for n > 0.
a(p) = 2 * p! for prime p.
MATHEMATICA
a[n_]:= n! * DivisorSum[n, 1/(# - 1)!^(n/# - 1) &]; a[0] = 1; Array[a, 22, 0] (* Amiram Eldar, Aug 22 2022 *)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(1-k*x^k/k!))))
(PARI) a(n) = if(n==0, 1, n!*sumdiv(n, d, 1/(d-1)!^(n/d-1)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 22 2022
STATUS
approved