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E.g.f. satisfies A(x) = (-log(1 - x / (1 - A(x))^2)) / (1 - A(x)).
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%I #14 Sep 08 2024 13:48:12

%S 0,1,7,116,3092,114034,5378396,309151968,20964872624,1638608258904,

%T 145038615271512,14340344355439200,1566483453363376896,

%U 187355848936261332144,24351019737412176648576,3417500066845923960657408,515071814323666902383222784

%N E.g.f. satisfies A(x) = (-log(1 - x / (1 - A(x))^2)) / (1 - A(x)).

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

%F a(n) = Sum_{k=1..n} (2*n+2*k-2)!/(2*n+k-1)! * |Stirling1(n,k)|.

%F E.g.f.: Series_Reversion( (1 - x)^2 * (1 - exp(-x * (1 - x))) ).

%o (PARI) a(n) = sum(k=1, n, (2*n+2*k-2)!/(2*n+k-1)!*abs(stirling(n, k, 1)));

%Y Cf. A052851, A371327, A376041.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Sep 07 2024