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%I #12 Mar 18 2024 12:52:08
%S 1,0,0,6,12,20,1470,12642,70616,2131992,39352410,470186750,
%T 11032124532,295053244356,5896487364950,146264289411450,
%U 4625791393554480,130492119237611312,3837833086814864946,135471306780659593206,4800394977109827314060
%N E.g.f. satisfies A(x) = 1/(1 - x^2*(exp(x*A(x)) - 1)).
%F a(n) = n! * Sum_{k=0..floor(n/3)} (n-k)! * Stirling2(n-2*k,k)/( (n-2*k)! * (n-2*k+1)! ).
%o (PARI) a(n) = n!*sum(k=0, n\3, (n-k)!*stirling(n-2*k, k, 2)/((n-2*k)!*(n-2*k+1)!));
%Y Cf. A370989, A371139.
%Y Cf. A358013, A371302.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Mar 18 2024
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