A354900 - OEIS

%I #15 Jun 11 2022 07:52:33

%S 1,9,163,6193,375001,33602521,4150656721,676462516801,140587148681281,

%T 36288005670120961,11388728893445164801,4270826391670469473921,

%U 1886009588552176549862401,968725766890781857146309121,572622616354852243874626732801

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

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

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

%t a[n_] := n! * DivisorSum[n, #^#/(n/#)! &]; Array[a, 15] (* _Amiram Eldar_, Jun 11 2022 *)

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

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, k^k*(exp(x^k)-1))))

%Y Cf. A057625, A354843, A354888, A354892, A354899.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jun 11 2022