A356667 Expansion of e.g.f. Sum_{k>=0} x^k / (1 - k*x^k/k!).

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

Links

Table of n, a(n) for n=0..21.

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

Cf. A356632, A356633, A356634.

Cf. A356668.

Sequence in context: A009621 A335907 A013195 * A323295 A166746 A052558

Adjacent sequences: A356664 A356665 A356666 * A356668 A356669 A356670

Keyword

nonn

Author

Seiichi Manyama, Aug 22 2022

Status

approved