A354845 - OEIS

%I #15 Jun 10 2022 11:08:03

%S 1,3,7,49,121,2281,5041,134401,907201,13184641,39916801,3753509761,

%T 6227020801,393409336321,7638997766401,160474477363201,

%U 355687428096001,75792615407308801,121645100408832001,32459310892353945601,475723576423839744001,7306033564948620902401

%N a(n) = n! * Sum_{d|n} (n/d)^(d-1) / d!.

%H Seiichi Manyama, <a href="/A354845/b354845.txt">Table of n, a(n) for n = 1..447</a>

%F E.g.f.: Sum_{k>0} (exp(k * x^k) - 1)/k.

%F If p is prime, a(p) = 1 + p!.

%t a[n_] := n! * DivisorSum[n, (n/#)^(#-1)/#! &]; Array[a, 20] (* _Amiram Eldar_, Jun 08 2022 *)

%o (PARI) a(n) = n!*sumdiv(n, d, (n/d)^(d-1)/d!);

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (exp(k*x^k)-1)/k)))

%Y Cf. A087906, A327578, A354843.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jun 08 2022