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%I #9 Mar 11 2024 06:08:19
%S 1,0,0,6,12,20,750,7602,47096,589752,11823930,169812830,2287327812,
%T 46793930196,1061518458182,21163158296490,458344052450160,
%U 12165772611938672,329982890581149426,8764089834124752822,255655700917556204540,8220667673623130347020
%N E.g.f. satisfies A(x) = 1 + x^2*(exp(x*A(x)) - 1).
%F a(n) = n! * Sum_{k=0..floor(n/3)} Stirling2(n-2*k,k)/(n-3*k+1)!.
%t nmax = 20; CoefficientList[Series[1 - x^2 - ProductLog[-E^(x*(1 - x^2))*x^3]/x, {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Mar 11 2024 *)
%o (PARI) a(n) = n!*sum(k=0, n\3, stirling(n-2*k, k, 2)/(n-3*k+1)!);
%Y Cf. A000272, A371115.
%Y Cf. A371118.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Mar 11 2024
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