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%I #6 Mar 30 2024 02:32:44
%S 1,-2,0,10,-4,-42,-258,306,5980,3142,61730,-794334,-3299074,-8459830,
%T 40220390,1550926110,1631691740,43693916390,-125593997262,
%U -4079362135854,-32054212967294,-33715330874838,-600410923342450,9383532800084966,329821022627776798
%N Expansion of e.g.f. Product_{k>=1} (1 - x^k/k!)^2.
%t nmax = 24; CoefficientList[Series[Product[(1 - x^k/k!)^2, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A002107, A032312, A185895, A371552.
%K sign
%O 0,2
%A _Ilya Gutkovskiy_, Mar 27 2024