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Expansion of e.g.f. ( (1/x) * Series_Reversion( x*(1 + log(1-x))^3 ) )^(2/3).
1

%I #11 Sep 22 2024 11:15:37

%S 1,2,20,388,11382,449868,22427988,1351746912,95626268208,

%T 7769995319280,713229439560816,73000860715645344,8243857485642410400,

%U 1018250616169754862048,136561871538665054975520,19763248903874313555142656,3069876028020976768409255808,509447295061343606934940250880

%N Expansion of e.g.f. ( (1/x) * Series_Reversion( x*(1 + log(1-x))^3 ) )^(2/3).

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

%F E.g.f.: B(x)^2, where B(x) is the e.g.f. of A367139.

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

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((serreverse(x*(1+log(1-x))^3)/x)^(2/3)))

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

%Y Cf. A367139, A376393.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Sep 22 2024