A354888 a(n) = n! * Sum_{d|n} d^d / d!.
1, 6, 33, 328, 3245, 52056, 828583, 17328256, 389416329, 10105386400, 285351587411, 8955841614336, 302881333613053, 11126513414294656, 437935136609883375, 18455736024587862016, 827240617573764860177, 39353706314004951028224
Offset: 1
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..386
Programs
-
Mathematica
a[n_] := n! * DivisorSum[n, #^#/#! &]; Array[a, 18] (* Amiram Eldar, Jun 10 2022 *)
-
PARI
a(n) = n!*sumdiv(n, d, d^d/d!);
-
PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (k*x)^k/(k!*(1-x^k)))))
Formula
E.g.f.: Sum_{k>0} (k * x)^k/(k! * (1 - x^k)).
If p is prime, a(p) = p^p + p! = A053042(p).