%I #9 Mar 06 2024 08:00:00

%S 1,1,1,3,12,54,432,2862,29880,311688,3530952,52947432,694960560,

%T 12339656640,208855024128,3885592056624,84031138091520,

%U 1688108258868480,41851910546369280,986544325475565696,25610732492679696384,720669291974958124800,19681263432530494848000

%N Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - log(1+3*x)/3) ).

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

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

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-log(1+3*x)/3))/x))

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

%Y Cf. A198860, A370936.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Mar 06 2024