%I #10 Dec 04 2023 06:36:03
%S 1,0,4,6,104,490,7452,65534,1062224,13825746,252414020,4303920742,
%T 89701635960,1870259792570,44391086228972,1085906907998670,
%U 29112549152845472,813723252665063842,24402507959486170260,765358519469125339190
%N Expansion of e.g.f. 1/(1 - 2 * x * (exp(x) - 1)).
%F a(0) = 1; a(n) = 2 * n * Sum_{k=2..n} binomial(n-1,k-1) * a(n-k).
%F a(n) = n! * Sum_{k=0..floor(n/2)} 2^k * k! * Stirling2(n-k,k)/(n-k)!.
%o (PARI) a(n) = n!*sum(k=0, n\2, 2^k*k!*stirling(n-k, k, 2)/(n-k)!);
%Y Cf. A052848, A367881.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Dec 03 2023
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