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%I A357392 #16 Sep 10 2024 04:20:07
%S A357392 0,1,5,56,990,24024,742560,27907200,1235591280,62990928000,
%T A357392 3634245014400,234102016512000,16654322805120000,1296884927852236800,
%U A357392 109720581991308288000,10021650950985427353600,982869376029609100032000,103017324974226408345600000
%N A357392 E.g.f. satisfies A(x) = -log(1 - x * exp(2 * A(x))).
%H A357392 <a href="/load/view.php?a=aHR0cDovL29laXMub3JnL2luZGV4L1JlcyNyZXZlcnQ">Index entries for reversions of series</a>
%F A357392 E.g.f. satisfies A(x) = log(1 + x * exp(3 * A(x))).
%F A357392 a(n) = Sum_{k=1..n} (2 * n)^(k-1) * |Stirling1(n,k)|.
%F A357392 a(n) = Sum_{k=1..n} (3 * n)^(k-1) * Stirling1(n,k).
%F A357392 a(n) = Product_{k=2*n+1..3*n-1} k = (3*n-1)!/(2*n)! for n > 0.
%F A357392 E.g.f.: Series_Reversion( exp(-3*x) * (exp(x) - 1) ). - _Seiichi Manyama_, Sep 10 2024
%o A357392 (PARI) a(n) = sum(k=1, n, (2*n)^(k-1)*abs(stirling(n, k, 1)));
%o A357392 (PARI) a(n) = sum(k=1, n, (3*n)^(k-1)*stirling(n, k, 1));
%o A357392 (PARI) a(n) = if(n==0, 0, (3*n-1)!/(2*n)!);
%Y A357392 Cf. A006963, A357393.
%Y A357392 Cf. A357333, A357338.
%K A357392 nonn
%O A357392 0,3
%A A357392 _Seiichi Manyama_, Sep 26 2022

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