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E.g.f. satisfies A(x) = 1 - x^2*A(x)^2*log(1 - x*A(x)).
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%I #12 Sep 19 2024 11:06:22

%S 1,0,0,6,12,40,2340,18648,154560,5767200,95911200,1438778880,

%T 48014778240,1228487644800,27997623029376,972327510000000,

%U 32550437645107200,1006902423902269440,38894136241736494080,1569697954634035537920,61093442927846310912000

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

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

%F a(n) = (n!)^2 * Sum_{k=0..floor(n/3)} |Stirling1(n-2*k,k)|/( (n-2*k)! * (n-k+1)! ).

%F E.g.f.: (1/x) * Series_Reversion( x/(1 - x^2*log(1 - x)) ). - _Seiichi Manyama_, Sep 19 2024

%o (PARI) a(n) = n!^2*sum(k=0, n\3, abs(stirling(n-2*k, k, 1))/((n-2*k)!*(n-k+1)!));

%Y Cf. A370994, A371118.

%Y Cf. A371121.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Mar 12 2024