%I #14 Dec 11 2021 04:29:26
%S 1,0,1,-3,-10,410,42985,-6527829,-24060996846,-6613442955828,
%T 3882375189467092921,235121650953066124724477,
%U -289337164954511885810252000250,-995208334663809003504695464745010282,13325880481925983143500510271865447222057073
%N a(n) = Sum_{k=0..n} (-1)^(n-k) * k^(k*(n-k)).
%H Seiichi Manyama, <a href="/A349894/b349894.txt">Table of n, a(n) for n = 0..52</a>
%F G.f.: Sum_{k>=0} x^k/(1 + k^k * x).
%o (PARI) a(n) = sum(k=0, n, (-1)^(n-k)*k^(k*(n-k)));
%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1+k^k*x)))
%Y Cf. A349856, A349857, A349858, A349891, A349893.
%K sign
%O 0,4
%A _Seiichi Manyama_, Dec 04 2021