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%I #9 Feb 20 2022 06:43:36
%S 1,1,0,6,36,-1240,36810,-743568,-4441640,2126086272,-201265464330,
%T 13670088101120,-512174277963612,-50655591400627200,
%U 16935777106057251442,-2936123018591228282880,368896773292405165345200,-22278163772113766968557568
%N a(n) = n! * Sum_{k=0..n} (-k * (n-k))^k/k!.
%t a[n_] := n!*(1 + Sum[(-k*(n - k))^k/k!, {k, 1, n}]); Array[a, 18, 0] (* _Amiram Eldar_, Feb 19 2022 *)
%o (PARI) a(n) = n!*sum(k=0, n, (-k*(n-k))^k/k!);
%Y Cf. A351780, A351795.
%K sign
%O 0,4
%A _Seiichi Manyama_, Feb 19 2022
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