A370579 - OEIS

%I #10 Feb 23 2024 09:02:49

%S 1,4,9,52,125,1806,5047,87368,544329,7408810,39916811,1281329292,

%T 6227020813,174477663374,2015997984015,45336862771216,355687428096017,

%U 16059446167564818,121645100408832019,5372665305815808020,76707372899469312021,2248001765299683993622

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

%F a(n) = n * A087906(n).

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

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

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

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

%Y Cf. A087906, A370580.

%Y Cf. A370602, A370603.

%K nonn,easy

%O 1,2

%A _Seiichi Manyama_, Feb 23 2024