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Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + log(1-x))^3 ).
4

%I #12 Sep 22 2024 11:15:34

%S 1,3,33,669,20130,808902,40799514,2480325810,176637134184,

%T 14428585258896,1330156753687152,136632403748954088,

%U 15476220160149512160,1916493979349783418192,257601843144279267685056,37352685483321694825767120,5812026059839341212943591168,965974072760231560672817681280

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

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

%F E.g.f. A(x) satisfies A(x) = 1/(1 + log(1 - x*A(x)))^3.

%F E.g.f.: B(x)^3, where B(x) is the e.g.f. of A367139.

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

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+log(1-x))^3)/x))

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

%Y Cf. A367139, A376394.

%Y Cf. A354122.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Sep 22 2024