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a(n) = (n-1)! * Sum_{d|n} d/(d-1)!.
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%I #8 Feb 23 2024 11:02:51

%S 1,3,5,22,29,546,727,18488,100809,1164250,3628811,208232652,479001613,

%T 18741602894,236107872015,4796881689616,20922789888017,

%U 1618457192352018,6402373705728019,471378116297088020,6105908234409984021,153272981387362636822

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

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

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

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

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

%Y Cf. A087906, A370579.

%K nonn,easy

%O 1,2

%A _Seiichi Manyama_, Feb 23 2024