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

%I #8 Aug 29 2024 11:24:35

%S 1,1,2,6,36,240,1800,16800,178080,2086560,27518400,399168000,

%T 6286896000,107623676160,1984274772480,39143052748800,824445099878400,

%U 18450791322163200,437015358530150400,10929450232744243200,287728555881102336000,7952251084537503744000

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

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

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+log(1-x^3)/x^2)))

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

%Y Cf. A007840, A375798.

%Y Cf. A353223.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 29 2024