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%I #10 Sep 21 2024 07:45:34
%S 1,0,0,6,0,60,2880,1680,201600,8074080,19958400,1824197760,
%T 69854400000,436929292800,36099561738240,1392369634656000,
%U 17026966410854400,1344523178718720000,54023115000830976000,1095484919871908966400,84994409643640713216000,3650011125774294048768000,109122812080533877712486400
%N Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x*log(1-x^2)) ).
%H <a href="/index/Res#revert">Index entries for reversions of series</a>
%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} (2*n-2*k)! * |Stirling1(k,n-2*k)|/k!.
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+x*log(1-x^2)))/x))
%o (PARI) a(n) = sum(k=0, n\2, (2*n-2*k)!*abs(stirling(k, n-2*k, 1))/k!)/(n+1);
%Y Cf. A370993, A376346.
%Y Cf. A370994, A375561.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Sep 21 2024