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E.g.f. satisfies A(x) = -log(1 - x * exp(3 * A(x))).
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%I #17 Sep 10 2024 04:21:51

%S 0,1,7,110,2730,93024,4037880,213127200,13253058000,948964262400,

%T 76899763100160,6957624460550400,695236239163065600,

%U 76043127767523840000,9036546669251861760000,1159342449440429270016000,159708538424128885551360000,23512778013219939149561856000

%N E.g.f. satisfies A(x) = -log(1 - x * exp(3 * A(x))).

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

%F E.g.f. satisfies A(x) = log(1 + x * exp(4 * A(x))).

%F a(n) = Sum_{k=1..n} (3 * n)^(k-1) * |Stirling1(n,k)|.

%F a(n) = Sum_{k=1..n} (4 * n)^(k-1) * Stirling1(n,k).

%F a(n) = Product_{k=3*n+1..4*n-1} k = (4*n-1)!/(3*n)! for n > 0.

%F E.g.f.: Series_Reversion( exp(-4*x) * (exp(x) - 1) ). - _Seiichi Manyama_, Sep 10 2024

%o (PARI) a(n) = sum(k=1, n, (3*n)^(k-1)*abs(stirling(n, k, 1)));

%o (PARI) a(n) = sum(k=1, n, (4*n)^(k-1)*stirling(n, k, 1));

%o (PARI) a(n) = if(n==0, 0, (4*n-1)!/(3*n)!);

%Y Cf. A006963, A357392.

%Y Cf. A357334.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Sep 26 2022