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

%I #11 Feb 23 2024 11:02:40

%S 1,3,4,17,6,307,8,5049,30250,105851,12,25945933,14,77837775,

%T 14529715216,147891744017,18,13435316294419,20,7606841430988821,

%U 16895152834560022,183030822374423,24,387276381308571955225,5385836820601036800026,485735643993600027

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

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

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

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

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

%Y Cf. A121860, A370579, A370580.

%K nonn,easy

%O 1,2

%A _Seiichi Manyama_, Feb 23 2024